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CORNELL 

UNIVERSITY 

LIBRARY 




CHEMISTRY 



Cornell University Library 

QD 564.K91 



The properties of electrically conductin 




3 1924 004 548 362 




Cornell University 
Library 



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tine Cornell University Library. 

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THE PROPERTIES OF 
ELECTRICALLY CONDUCTING 

SYSTEMS 

Including Electrolytes and Metals 



BY 

CHARLES A. KRAUS 

PROFESSOR OP CHEMISTRY IN CLARK UNIVERSITY 



WITH 70 FIGURES IN THE TEXT 




American Chemical Society 
Monograph Series 



BOOK DEPARTMENT 
The CHEMICAL CATALOG COMPANY, Inc. 

ONE MADISON AVENUE, NEW YORK, U. S. A, 
1922 



Copyright, 1922, By 

The CHEMICAL CATALOG COMPANY, Inc. 

All Rights Reserved 



Press of 

J. J. Little & Ives Company 

New York, U. S. A. 



GENERAL INTRODUCTION 

American Chemical Society Series ''of 
Scientific and Technologic Monographs 

By arrangement with the Interallied Conference of Pure and Applied 
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3 



4 GENERAL INTRODUCTION 

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Two rather distinct purposes are to be served by these monographs. 
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GENERAL INTRODUCTION 
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PREFACE 

The history of the development of chemistry and molecular physics 
during the past few decades is largely an account of the growth of our 
conceptions of matter in the ionic condition. Whatever the shortcomings 
of the older ionic theory may have been, it has proved itself a powerful 
tool for the purpose of disclosing the structure of material substances. 
The intimate relation existing between matter and electricity, first in- 
ferred by Helmholtz as a consequence of Faraday's laws, has been estab- 
lished as securely as the atomic theory itself. Present day conceptions 
as to the nature of matter are, in a large measure, the outgrowth of 
fundamental conceptions underlying the ionic theory. It is true that 
certain branches of molecular physics, to the development of which the 
ionic theory has contributed, have outstripped this theory in the impor- 
tance of the results obtained. Nevertheless, the further advance of 
chemistry is largely dependent upon the further development of our con- 
ceptions of matter in the ionic condition. 

A vast amount of experimental material relating to this subject has 
accumulated during the past thirty years. It is found scattered through 
the volumes of many journals and the transactions of scientific societies. 
Unfortunately, this material has nowhere been collected in a form ren- 
dering it available to those who are not primarily interested in this field. 
The purpose of the present volume is to present the more important of 
this material in a comprehensive and systematic manner, thus enabling 
the reader to gain a knowledge of the contemporary state of this subject 
without an undue expenditure of time and effort. It is hoped, too, that 
this volume will prove useful to those investigators in allied sciences, who 
find it diflScult to ascertain the precise limitations underlying methods 
and ideas which they often find it necessary to apply in their own 
subjects. 

The systems treated are those in which ionic phenomena are most 
clearly in evidence. Metallic systems are included, for, although the 
nature of the metals is but little understood, the existence of a relation 
between the phenomena in metallic and electrolytic systems is unmis- 
takable. The treatment of metals is necessarily brief, since our knowl- 
edge of them is still very uncertain. The chemical aspects of metallic 
systems are, so far as possible, kept in the foreground. A more detailed 

7 



8 PREFACE 

treatment of the experimental material relating to metals is unnecessary, 
since much of this has already been collected in various handbooks. 

Naturally, the major portion of this volume is devoted to a con- 
sideration of the properties of electrolytic solutions. The attempt has 
been made to present the subject broadly in order to bring out those 
elements of the phenomena which are common to solutions in all solvents. 
Solutions in non-aqueous solvents are treated somewhat more extensively 
than aqueous solutions, since the data relating to these solutions have 
not been collected heretofore. 

The subject is presented from an empirical standpoint, since an ade- 
quate theory of electrolytic solutions does not exist. Such theories as 
have been advanced in recent years give evidence of having been adapted 
to fit particular cases. In the end, the theory of electrolytic solutions 
will probably be a composite of various theories which now appear more 
or less applicable. Such a theory will doubtless embody some of the 
more fundamental elements of the older ionic theory. 

A complete bibliography has not been attempted. References given 
as footnotes will serve as a key to the literature. 

In conclusion, I wish to express my indebtedness to my colleague. 
Professor B. S. Merigold, for reading the manuscript and to Mr. Gordon 
W. Browne for his assistance in preparing the figures. 

C. A. K. 

Clark University, 
January 5, 1922. 



CONTENTS 

f^HAPTEn PACK 

I. Introduction 13 

1. Classification of Conductors. 2. Gases. 3. Metallic 
Conductors. 4. Electrolytic Conductors; a. Electrolytes 
Which Conduct in the Pure State; b. Electrolytic Solutions. 
5. Electricity and Matter. 6. The Ionic Theory. 

II. Elementary Theory op the Conduction Process in Elec- 

trolytes 19 

1. Material Effects Accompanying the Conduction Process. 
2. Concentration Changes Accompanying the Current: 
Hittorf's Numbers. 3. The Conductance ^of Electrolytic 
Solutions. 4. Ionization of Electrolytes. | 5. Molecular 
Weight of Electrolytes in Solution. 6. Applicability of the 
Law of Mass Action to Electrolytic Solutions. 



III. The Conductance of Electrolytic Solutions in Various 

Solvents 46 

1. Characteristic Forms of the Conductance-Concentration 
Curve. 2. Applicability of the Mass-Action Law to Non- 
Aqueous Solutions. 3. Comparison of the Ion Conductances 
in Different Solvents. 



IV. Form of the Conductance Function 67 

1. The Functional Relation between Conductance and 
Concentration. 2. Geometrical Interpretation of the Con- 
ductance Function. 3. Relation between the Properties of 
Solvents and Their Ionizing Power. 4. The Form of the 
Conductance Curve in Dilute Aqueous Solutions. 5. Solu- 
tions of Formates in Formic Acid. 6. The Behavior of Salts 
of Higher Type. 

V. The Conductance of Solutions as a Function of Their 

Viscosities 109 

1. Relation between the Limiting Conductance Ao and the 
Viscosity of the Solvent. 2. Change of Conductance as 
Result of Viscosity Change due to the Electrolyte Itself. 3. 

9 



10 CONTENTS 

CHAPTER PAGB 

Relation between Viscosity and Conductance on the Addition 
of Non-Electrolytes. 4. The Influence of Temperature on 
the Conductance of the Ions. 5. The Influence of Pressure 
on the Conductance of Electrolytic Solutions. 

VI. The Conductance of Electrolytic Solutions as a Func- 

tion OP Temperature 144 

1. Form of the Conductance-Temperature Curve. 2. 
Conductance of Aqueous Solutions at Higher Temperatures. 
3. The Conductance of Solutions in Non-Aqueous Solvents 
as a Function of the Temperature. 4. The Conductance of 
Solutions in the Neighborhood of the Critical Point. 

VII. The Conductance op Electrolytes in Mixed Solvents . 176 

1. Factors Governing the Conductance of Electrolytes in 
Mixed Solvents. 2. Conductance of Salt Solutions on the 
Addition of Small Amounts of Water. 3. The Conductance 
of the Acids in Mixtures of the Alcohols and Water. 4. Con- 
ductance in Mixed Solvents over Large Concentration Ranges. 



VIII. Nature op the Carriers in Electrolytic Solutions . . 198 

1. Interaction between the Ions and Polar Molecules. 2. 
Hydration of the Ions in Aqueous Solution. 3. Calculation 
of Ion Dimensions from Conductance Data. 4. The Hydro- 
gen and Hydroxyl Ions. 5. Ions of Abnormally High Con- 
ductance. 6. The Complex Metal-Ammonia Salts. 7. 
Positive Ions of Organic Bases. 8. Complex Anions. 9. 
Other Complex Ions. 

IX. Homogeneous Ionic Equilibria 218 

1. Equilibria in Mixtures of Electrolytes. 2. Hydro- 
lytic Equilibria. 



X. Heterogeneous Equilibria in Which Electrolytes Are 

Involved 232 

1. The Apparent Molecular Weight of Electrolytes in 
Aqueous Solution. 2. The Molecular Weight of Electrolytes 
in Non-Aqueous Solutions. 3. Solubility of Non-Electro- 
lytes in the Presence of Electrolytes. 4. Solubility of Salts 
in the Presence of Non-Electrolytes. 5. Solubility of Elec- 
trolytes in the Presence of Other Electrolytes ; a. Solubility of 
Weak Electrolytes in the Presence of Strong Electrolytes with 
an Ion in Common; b. The Solubility of Strong Binary Elec- 



CONTENTS 11 

CHAPTER 

trolytes in the Presence of Other Strong Electrolytes; c. The 
Solubility of Salts of Higher Type in the Presence of Other 
iiilectrolytes. 

XI. Other Properties op Electrolytic Solutions .... 280 
1 }•' T|ie Diffusion of Electrolytes. 2. Density of Electro- 
^tic Solutions. 3. Velocity of Reactions as Affected by the 
Presence of Ions. 4. Optical Properties of Electrolytic Solu- 
tions^ 5. The Electromotive Force of Concentration Cells. 

t i'^^™^! P^Perties of Electrolytic Solutions. 7. Change 
of the Transference Numbers at Low Concentrations. 8. 
Reactions in Electrolytic Solutions. 9. Factors Influencing 
ionization; a. The Ionizing Power of Solvents in Relation to 
I heir Constitution; b. The Relation between the Ionization 
Process and the Constitution of the Electrolyte. 

XII. Theories Relating to Electrolytic Solutions . . . 323 

1. Outline of the Problem Presented by Solutions of Elec- 
trolytes. 2. Electrolytic Solutions from the Thermodynamic 
Point of View; a. Scope of the Thermodynamic Method; b. 
Jahn's Theory of Electrolytic Solutions; c. Comparison of the 
Thermodynamic Properties of Electrolytes; Inconsistencies in 
the Older Ionic Theory; The Thermodynamic Method; 
Numerical Values; Solubility Relations According to Bronsted. 
3. Theories Taking into Account the Interionic Forces; a. 
Theory of Malmstrom and Kjellin; b. Theory of Ghosh; c. 
Milner's Theory; d. Hertz's Theory of Electrolytic Conduc- 
tion. 4. Miscellaneous Theories. 5. Recapitulation. 

XIII. Pure Substances, Fused Salts, and Solid Electrolytes 351 
1. Substances Having a Low Conducting Power. 2. 

Fused Salts. 3. Conductance of Glasses. 4. Solid Elec- 
trolytes. 5. Lithium Hydride. 

XIV. Systems Intermediate between Metallic and Electro- 

lytic Conductors 366 

1. Distinctive Properties of Metallic and Electrolytic Con- 
ductors. 2. Nature of the Solutions of the Metals in Am- 
monia. 3. Material Effects Accompanying the Current. 4. 
The Relative Speed of the Carriers in Metal Solutions. 5. 
Conductance of Metal Solutions. 

XV. The Properties of Metallic Substances 384 

1. The Metallic State. 2. The Conduction Process in 
Metals. 3. The Conductance of Elementary Metallic Sub- 



12 CONTENTS 

stances. 4. The Conductance of Elementary Metals as a 
Function of Temperature. 5. The Conductance of Metallic 
Alloys; a. Heterogeneous Alloys; b. Homogeneous Alloys; c. 
Solid Metallic Compounds; d. Liquid Alloys. 6. Variable 
Conductors. 7. The Conductance of Metals as Affected by 
Other Factors; a. Anisotropic Metallic Conductors; b. Influ- 
ence of Mechanical and Thermal Treatment; c. The Influence 
of Pressure on Conductance; d. Photo-Electric Properties. 
8. Relation between Thermal and Electrical Conductance in 
Metals. 9. Thermoelectric Phenomena in Metals. 10. 
Galvanomagnetic and Thermomagnetic Properties. 11. Op- 
tical Properties of Metals. 12. Theories Relating to Metallic 
Conduction. 

Indices 409 



THE PROPERTIES OF ELECTRICALLY 
CONDUCTING SYSTEMS 

Chapter I. 
Introduction. 

1. Classification of Conductors. The property of electrical con- 
ductance appears to be one common to all forms of matter. The value 
of the conductance of different forms of matter, however, varies within 
very wide limits. Thus, the specific conductance of silver has a value 
of 6.0 X 10=, while that of parafRn is 3.5 X 10-^°- The specific con- 
ductance of gases imder ordinary conditions is scarcely measurable. Nat- 
urally, the conductance of any given system depends upon its state; and, 
in general, any change in the condition of the system will materially 
affect the value of its conductance. 

Conductors may be conveniently grouped into a number of classes, 
the members of which possess many properties in common. 

2. Gases. Under ordinary conditions the conducting power of gases 
is of a very low order, and such conductance as they possess is not an 
intrinsic property of the gases themselves, but is due, rather, to the in- 
fluence of external agencies. Thus, under the action of various radia- 
tions, gases are ionized and when in this condition conduct the current. 
This power of conduction, however, is lost when the external source of 
excitation is cut off. Whether or not the gases themselves may possess 
in some slight degree the power of conducting the current is uncertain, 
since the conducting power of gases which have been entirely freed from 
disturbing effects is of such a low order that the usual methods of meas- 
urements fail. The conductance of a gas is a function of its density. 
It is probable that at high densities gases will exhibit properties com- 
parable with those of many liquids. In the case of hexane it has been 
shown that the residual conductance on purification is for the most part 
due to the action of external radiations, which indicates that the con- 
ductance, which many liquid substances of low conducting power possess, 
is not a property of the pure substances themselves. 

In gases, as well as in insulating liquids, under the action of external 

13 



14 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

radiations, we have systems which are not in a state of equihbnum. 
These systems will not be further considered here, since they have been 
treated extensively in treatises dealing with the conduction of gaseous 
systems. In what follows we shall treat only such systems as are nor- 
mally in a conducting state. These may be divided into two classes; 
namely, metallic and electrolytic conductors. 

3. Metallic Conductors. Metallic conductors are characterized by 
the absence of material effects when a current passes through a system 
comprising one or more conductors of this class alone. In this respect 
metallic conductors are for the most part sharply differentiated from 
electrolytic conductors, in which concentration changes or other material 
effects accompany the passage of the current through any surface of 
discontinuity. It does not follow, however, that metallic and electro- 
lytic conduction are entirely unrelated and that the two processes of 
conduction may not take place more or less simultaneously. Certain 
substances apparently conduct electrolytically when in one condition and 
metallically when in another. In other cases, a portion of the current 
appears to be carried by a process similar to that in the metals and 
another portion by a process similar to that in electrolytes. 

Metallic conductors are also characterized by the relatively high 
value of their conducting power. While a few metals exhibit a value 
of the conductance comparable with that of electrolytes, the conductance 
of most metals is many times greater than that of electrolytes. If this 
is true at ordinary temperatures, it is even more true at lower tempera- 
tures where the resistance may ultimately fall off to practically zero. 
The problem of metallic conduction is one possessing great interest and 
one whose solution cannot but prove to be of great importance in the 
development of chemistry and molecular physics. At the present time, 
however, its solution appears far from complete. While metallic con- 
ductors come within the scope of the present monograph, it is not in- 
tended to treat this subject exhaustively. 

4. Electrolytic Conductors. Electrolytic conductors are character- 
ized, in the first place, by the fact that the passage of the current through 
them is accompanied by a transfer of matter. In a homogeneous elec- 
trolytic conductor this transfer of matter within the body of the con- 
ductor does not become apparent, but at any point of discontinuity 
material effects make their appearance. The material effects accom- 
panying the current are subject to certain definite laws commonly known 
as Faraday's Laws. Conductors for which Faraday's Laws hold true 
within the limits of the experimental error are termed electrolytic con- 
ductors. We have here to consider two classes of electrolytic conductors: 



INTRODUCTION 15 

First, those which conduct the current when in a pure state and, second, 
those which conduct the- current as a result of the presence of other sub- 
stances. This latter class of conductors is embraced within the term 
electrolytic solutions. 

a. Electrolytes Which Conduct in the Pure State. Within this class 
is included, in the first place, the fused salts. With a few exceptions, 
the fused salts are excellent conductors of the electric current. Their 
specific conductance near the melting point being of the order of 1.0, 
their conductance, therefore, is about 1 X 10"° that of silver. The salts 
are compounds between a strongly electronegative and a strongly electro- 
positive constituent, and it is seldom that such substances do not possess 
the power of conducting the current in a marked degree. As the electro- 
positive or electronegative nature of one or the other of the constituents 
becomes less pronounced, however, the conductance of the resulting 
compound is diminished. This is the case, for example, with mercuric 
chloride. 

When hydrogen is combined with a strongly electronegative element 
or group of elements, the resulting compound, as a rule, exhibits electro- 
lytic properties. This, for example, is the case with water, which has 
been shown to conduct the current slightly when in a pure state. At 
18° its specific conductance has a value of 0.042 X 10"*. Other com- 
pounds of hydrogen exhibit similar properties. 

When hydrogen is combined with elements which are less strongly 
electronegative, the resulting compounds exhibit a lower conducting 
power. In the case of the hydrocarbons the conductance reaches ex- 
tremely low values and it is possible that these substances in the pure 
state do not possess the power of conducting the current. 

While substances in the fused state are, as a rule, better conductors 
than in the solid state, electrolytic conductors are not restricted to the 
fused state, since certain substances in the solid state have been found 
to conduct the current quite as readily as the fused salts. 

b. Electrolytic Solutions. The most common electrical conductors 
are those in which the conductance is due to a mixture of two or more 
substances. As a rule, one of these, the solvent, is present in consider- 
able excess and may itself be only a very poor conductor. In this case, 
the conductance is said to be due to the addition of the second compo- 
nent, termed the electrolyte. To this class belong all the ordinary solu- 
tions of salts in water. In some cases an electrolytic solution results 
when a substance, which itself in the pure state is a poor conductor, is 
added to a second substance which likewise is a poor conductor in the 
pure state. As an example, we may cite solutions of the acids in water. 



16 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Hydrochloric acid, for example, in the pure state has a conductance even 
lower than that of water. When dissolved in water, however, the con- 
ductance of hydrochloric acid is much greater than that of ordinary salts 
dissolved in the same solvent. This class also includes solutions of 
various organic oxygen and nitrogen compounds in the liquid halogen 
acids. This behavior, moreover, is not restricted to acids, since solu- 
tions of many bases, such as ammonia, result from a mixture of two 
components neither of which possesses considerable conductance in the 
pure state. Where an electrolytic solution results from a mixture of two 
components which are themselves non-conductors, it is probable that 
reaction takes place when the two components are brought together, as 
a result of which an electrolyte is formed. 

Apparently, electrolytic solutions result in all cases when typical 
salts are dissolved in liquids up to sufficiently high concentrations. The 
property of forming electrolytic solutions with dissolved salts is thus 
not peculiar to water or solvents of the water type, but is a property 
common to all fluid media. It is true that the phenomena are materially 
altered as the nature of the solvent medium changes, but otherwise, if 
the solutions are sufficiently concentrated, the order of the conductance 
values will not differ greatly in different solvents. 

Among the various properties of the solvent medium which appear 
to have a marked influence upon the properties of the resulting electro- 
lytic solution, the dielectric constant stands out as the most important 
factor. As the dielectric constant of the solvent medium decreases, the 
conductance of the resulting solutions is altered, but the power to con- 
duct the current is never lost, no matter how low the dielectric constant 
of the solvent medium may be. Thus, solutions of salts of organic bases 
in chloroform conduct fairly well. 

From the standpoint of the development of chemistry, solutions of 
electrolytes are of first-rate importance. Electrolytic solutions exhibit a 
variety of phenomena and admit of a variety of reactions which are not 
to be found in the case of any other system of substances. A great 
variety of reactions take place at the electrodes when solutions of elec- 
trolytes are electrolyzed, and, when solutions of electrolytes are mixed 
reactions take place between the constituent electrolytes. Reactions be- 
tween electrolytes are characterized by the extreme facility with which 
they occur. It is only in exceptional cases that the rate of such reac- 
tions is sufficiently low to admit of measurement. In solutions of elec- 
trolytes, therefore, we are dealing essentially with systems in equilibrium. 
This is of importance in their theoretical treatment, since thermodynamic 
principles may be readily applied to systems in equilibrium. 



INTRODUCTION 17 

5. Electricity and Matter. While electrolytic solutions are thus of 
great importance from a practical point of view, they have played no 
less important a role in the development of our conceptions of the nature 
of matter and the nature of chemical reactions. That electricity and 
matter are intimately related was long since pointed out by Helmholtz 
as a consequence of Faraday's Law. Since in electrolytes electricity and 
matter are associated in definite and fixed proportions, and since matter 
appears to be discrete in its structure, it follows that electricity also must 
be discrete in its fundamental structure. Corresponding to the atoms, 
the smallest subdivisions of elementary substances, we have the funda- 
mental charge of electricity, the charge associated with a single univa- 
lent ion, which represents the smallest known subdivision of the electric 
charge. The development of the mechanics of the atoms in the last two 
decades has greatly enlarged our knowledge of the fundamental relation 
between electricity and matter. The fundamental charge of electricity, 
the charge associated with the negative electron, is objectively as real as 
the atoms and the molecules themselves. The intimate relation of the 
fundamental charge with the atoms or groups of atoms, which play so 
important a part in many chemical reactions, makes it appear probable 
that in chemical reactions the negative electron is primarily concerned. 
The horizon of chemistry is rapidly broadening in this direction, and a 
study of electrolytic systems will unquestionably play a great part in 
the ultimate elucidation of the mechanics of chemical reactions. 

6. The Ionic Theory. To account for the various phenomena which 
have been observed in electrolytic solutions, the ionic theory has been 
introduced. While ordinarily the ionic theory is supposed to include 
fundamentally those concepts first introduced by Arrhenius, this theory 
is, in fact, a composite theory in which many molecular mechanical 
hypotheses are combined. It is to Arrhenius that is due the credit of 
first having developed a theory of electrolytes, quantitative in its nature, 
the correctness of which it was possible to determine by exact quantita- 
tive methods. While the gaps left in the theory of electrolytic solutions 
by the work of Arrhenius may not be overlooked, it should not be for- 
gotten that up to the present time no other theory has been proposed 
which is equally well able to account for so many and for so large a 
variety of facts. 

The introduction of the theory of Arrhenius has, from the start, met 
with the most determined opposition on the part of many chemists. It 
is interesting, now, to note that in recent years the basis of the objections 
to the theory of Arrhenius has greatly shifted and many of the originally 
proposed objections have since been found to be without foundation. 



18 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Nevertheless, the opposition to the theory of Arrhenius has continued to 
find supporters even up to the present time. In part, at least, this oppo- 
sition has been due to a realization on the part of chemists of the limi- 
tations of the theory of which its author has himself been aware. One 
of the fundamental truths which the theory of Arrhenius has brought 
to the attention of chemists is the existence of equilibria in electrolytic 
systems; and, however the details of his theory may subsequently be 
modified, it would appear that this most fundamental element of his 
theory must always be retained. 



Chapter II. 

Elementary Theory of the Conduction Process in 
Electrolytes. 

1. Material Effects Accompanying the Conduction Process. That 
material effects accompany the passage of the current through a non- 
metallic medium was known at an early date. Thus Nicholson and 
Carlisle ^ observed the decomposition of water, and Sir Humphrey Davy '■' 
isolated the element potassium by electrolysis of the hydroxide. While 
it was thus recognized that chemical action is intimately associated with 
the passage of the current through an electrolyte, the quantitative rela- 
tionships were not studied until Faraday carried out his classical re- 
searches. It is unnecessary to give here in detail the results of Faraday's 
investigations. It will be sufficient to state the laws which now bear his 
name; namely, that chemical action accompanying the passage of the 
current is proportional to the quantity of electricity passing, and that, 
for a given quantity of electricity, the chemical effects in the case of 
different reactions are equivalent. These laws have since been verified 
by a multitude of observations on the action of the current passing 
through electrolytes. The most exact measurements have been made 
on the deposition of silver and on the liberation of iodine.^ In all cases, 
Faraday's Law has been found to hold within the limits of experimental 
error. It has been found to hold in the case of fused salts at higher tem- 
peratures,* as well as in that of certain solid electrolytes." 

There are cases, indeed, where apparent exceptions to Faraday's Law 
appear. For example, when a current is passed through a solution con- 
taining a compound of sodium and lead in equilibrium with metallic 
lead, there are deposited on the anode 2.25 equivalents of lead per equiva- 
lent of electricity." Similar results have been obtained in the case of 
solutions of certain other metallic complexes in liquid ammonia.'' These 
cases however, do not constitute an exception to Faraday's Law, since 
there are present in these solutions, presumably, a series of complexes 

1 Nicholson and Carlisle, Nicholson's Jour. 4, 179 (1800) ; aUbert's Ann. 6, 340 (1800). 

> Bates ^TdVinai.V.'iTCTem. Soe. 36, 936 (1914). 
^mchlrds and Stuil, Proo. Am. Acad. « 409 (1902). 
•Tubandt and Lorenz, Ztschr. f. phys. Chem. 87. 513 (1914). 
• Smyth, J. Am. Chem. Soc. 39, 1299 (1917). 
'Pecli, J. Am. Chem. Soc. J/O, 335 (1918). 

19 



20 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

whose average composition corresponds to the reaction which occurs at 
the electrode on electrolysis of these solutions. The precipitation at the 
anode in these solutions corresponds to the average composition of the 
complex. 

The solutions of the alkali metals and the metals of the alkaline 
earths in liquid ammonia constitute another apparent exception to Fara- 
day's Law, and in order to reconcile the results obtained in the case of 
these solutions with Faraday's Law it is necessary to extend it.^ When, 
for example, a current is passed through a solution of sodium in liquid 
ammonia, only a fraction of the current appears to be accompanied by 
an observable material process. These solutions, therefore, behave as 
though the current were in part carried by an electrolytic and in part 
by a metallic process. In order to reconcile these results with Faraday's 
Law, it is necessary to assume that the process of metallic conduction is 
likewise an ionic one, the current in this case being carried by the nega- 
tive electrons. If this hypothesis is made, then Faraday's Laws hold in 
these cases also. 

Faraday's Laws lead to important conclusions, not only with regard 
to the mechanism of the conduction process in electrolytes, but also with 
regard to the relation between .electricity and matter. Interpreted from 
a molecular kinetic point of view, Faraday's Laws state that definite fixed 
quantities of electricity are associated with definite amounts of matter. 
As Helmholtz " pointed out, if matter consists of discrete particles, then 
electricity likewise is discrete in character. Corresponding to the atom, 
the smallest subdivision of matter, we have a fundamental electric 
charge, namely, the charge on a univalent ion. The charge, therefore, 
On any given particle of matter, whether it be of molecular or atomic 
dimensions or whether it be of larger dimensions as, for example, a drop 
of oil, may not be varied continuously but only in multiples of the unit 
charge. The discontinuous nature of the electric charge is one of the 
fundamental facts underlying electrochemical phenomena and must be 
taken into account in the interpretation of these phenomena. 

The reactions accompanying the passage of the current through an 
electrode surface indicate clearly that an intimate relation exists between 
chemical and electrical phenomena. Berzelius^" attempted to account 
for the structure of chemical compounds by means of an electrical 
hypothesis. In this, however, he was unsuccessful, largely because he 
assumed a false mechanism as representing the association between 
electricity and matter. Instead of associating the charge with the atoms 

'Kraus, J. Am. Chem. 8oc. SO, 1323 (1908) ; SB, 864 (1914) 
• Helmholtz, J. Chem. Soc. SB, 277 (1881) ; Wigs. Abh. S p "52 
"Berzelius, Lehrbuch, Ed. 3, Vol. 5 (1835) ; Ostwald, Electroohemie, p. 335 



CONDUCTION PROCESS IN ELECTROLYTES 21 

themselves, in his theory, he associated the charge with certain atomic 
complexes, which complexes in fact do not exist. Present day concep- 
tions regarding the constitution of chemical compounds do not differ in 
many respects from those of Berzelius save that it is assumed that the 
charge is associated with the atoms. In recent years, as a result of ex- 
perimental methods which have enabled us to gain an insight into the 
structure even of the atoms themselves, it is becoming more and more 
apparent that, in their compounds, the elements exist not in an atomic, 
but in an ionic, that is, in a charged, state. Under ordinary conditions 
this state of the elements in a compound is not clearly evidenced, except 
in the case of such compounds as are electrolytes when dissolved in 
suitable solvents or when in a fused state. From the standpoint of chem- 
istry, the study of the properties of electrolytes is therefore not so much 
an end as a means. In other words, the study of the properties of 
electrolytes constitutes a convenient method of acquiring knowledge 
regarding the constitution of various chemical compounds. 

Faraday was not content to merely state the results of his observa- 
tions and to combine these observations in the form of general laws. 
He attempted to gain an insight into the mechanism of the processes 
involved. It is often assumed that the ionic theory dates from the 
time when Arrhenius co-ordinated the work of earlier investigators and 
suggested a means for determining the relative amount of carriers present 
in an electrolytic solution under given conditions. The ionic theory, 
however, is much older than this. Its foundation was laid by Faraday ,^^ 
who recognized that in an electrolyte the current is carried by positive 
and negative electrical charges associated with definite material com- 
plexes moving in opposite directions through the solution. The terms 
which we now employ to describe the phenomena observed in the pas- 
sage of the current through an electrolyte are due to Faraday, and in 
themselves contain the concept of motion. The chief contribution of the 
later ionic theory consisted in devising methods which made it possible 
to determine the number of carriers present in an electrolytic solution. 
Whether or not these methods, in fact, give us a true measure of the 
number of ions present under various conditions in no wise affects the 
correctness of the more general conceptions upon which the ionic theory 

is based, . 

2. Concentration Changes Accompanying the Current: Hittorj s 
Numbers. The concentration changes in the neighborhood of the elec- 
trodes were first investigated by Hittorf.^^ The fundamental conception 

"Faraday, "Experimental Researches," Vol. 1. 
"Hittorf, Pogg. Ann. 89, 177 (1853). 



22 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

underlying these concentration changes is that, within the solution, the 
electric current is carried by positive and negative carriers which move 
with velocities proportional to the potential gradient existing in the 
solution. Within the body of the electrolyte itself. Ohm's law is obeyed. 
The observed concentration change at an electrode is thus the resultant 
of two effects; namely, loss or gain due to the reaction at the electrode 
and loss or gain due to the motion of the positively and negatively 
charged carriers. The simplest case is that in which precipitation of 
the ions takes place at the electrodes. Let us assume that the charge u 
is transported through the solution by the cation and the charge v by 

the anion. Then — ; — will be the fraction of the charge carried by the 
u-\-v 

positive ion and — ; — the fraction of the charge carried by the negative 

M + w 

ion. If one equivalent of material is precipitated at the cathode, then 

u and V will represent the number of equivalents of matter carried up 

to the electrodes as cation and anion respectively. The concentration 

change in the neighborhood of the cathode will correspond to a loss of 

one equivalent of the electrolyte due to precipitation at the electrode and 

u 
to a gain of — — — equivalents carried up to the electrode by the cations. 

The total observed concentration change, therefore, will be equal to the 

difference of these two or to a loss of — -j— equivalents. Similarly, 

u 
at the anode, the change will correspond to — -j- — equivalents. It is 

evident that, if the concentration change due to the passage of a given 

charge is known and if the nature of the electrode reactions is known, 

V u 

then the ratios , and — j — may be determined. These ratios, 

which Hittorf termed the "transference numbers" of the cation and anion, 
respectively, we shall denote by the symbols n and 1 — n. 

In determining the transference numbers of an electrolyte by the 
method of Hittorf, the concentration changes are measured with respect 
to water. In other words, the determination of these numbers is based 
upon the assumption that water itself remains at rest, and is in no wise 
concerned in the process of the transfer of electricity through the solution. 
We now know that this condition is not strictly fulfilled and that water 
plays a part in the conduction process. When a cmrent of electricity 
passes through an aqueous solution, the solvent itself is transferred to 
some extent along with the ions. Obviously, this will affect the concen- 



CONDUCTION PROCESS IN ELECTROLYTES 23 

tration changes observed at the electrodes. In order to determine the 
relative amounts of solvent transferred by the two ions, it is necessary 
that there should be present in the solution some reference substance 
which remains at rest when the current passes through the solution. The 
concentration changes may then be referred to this reference substance 
and the true transference numbers of the electrolyte determined, together 
with the relative amounts of water associated with the transfer of the 
charge through the solution. Since the results of such measurements will 
be discussed in detail in another chapter, it will be unnecessary to proceed 
further with their discussion here. They have been alluded to at this 
point merely for the purpose of calling attention to the fundamental 
assumption underlying the Hittorf method of determining transference 
numbers. 

That the passage of the current through an electrolyte is accompa- 
nied by a transfer of matter may also be shown by other means, as, for 
example, by introducing a surface of discontinuity " in the path of a 
conducting electrolyte. Such surfaces of discontinuity may be observed 
visually and thus yield a very direct method for demonstrating the trans- 
fer of matter by means of the current within the body of the electrolyte. 
If, for example, a solution containing hydrochloric acid is superimposed 
on a solution containing potassium chloride and a current is passed 
through the boundary of these solutions in such direction that the more 
rapidly moving ion, namely, in this case, the hydrogen ion, precedes 
the more slowly moving ion, the potassiimi ion, then the boundary be- 
tween the two solutions will advance in the direction of the positive 
current. The rate of motion of the boundary under a given potential 
gradient will depend upon the speed of the carriers. If a solution of an 
electrolyte is placed between solutions of two other electrolytes, each of 
which has one ion in common with the first, then, under the action of a 
potential, the two boundaries will move in opposite directions, the boun- 
dary between the cations moving toward the cathode and that between 
the anions toward the anode. It is of course necessary that the condi--^ 
tions for stability of theloundaries should be fulfilled. This requires 
that at each boundary the more rapidly moving ion shall move in ad- 
vance of the more slowly moving ion. Allowing for certain corrections 
which must be made, the ratio of the speeds of the two boundaries is 
proportional to the current carrying capacities of the two ions." 

While the method of moving boundaries may thus be employed for 
measuring the transference numbers of electrolytes, its chief value, per- 

"Lodge, Brit. Ass. Reports, p. 389 (1886). 
"Lewis, J. Am. Chem. Soc. 32, 863 (1910). 



24 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

haps, lies in that it enables us to observe the motion of the electrolyte 
within the solution visually. 

The results of transference measurements cannot be interpreted with- 
out a knowledge of the nature of the ions within the solution. The 
transference numbers are calculated from the observed concentration 
changes on an assumption as to the nature of the ions themselves. For 
example, in determining the transference numbers of potassium chloride 
by the Hittorf method, it is assumed that only potassium is transferred 
to the cathode and chlorine to the anode. If, however, ions different from 
those assumed exist in the solution, these will take part in the transfer 
of electricity and will have an influence upon the observed concentration 
changes at the electrodes. The question as to whether or not the ions 
have the simple structure commonly assumed is one which ultimately 
must be answered on the basis of considerations derived from other prop- 
erties of these solutions. That complex ions are formed in the case of 
certain solutions was conclusively shown by Hittorf.^" He found that 
in solutions of cadmium iodide the transference number of the cation, 
as measured, is greater than unity. Since this ion cannot transport 
more current than the total passing through the solution, it is obvious, as 
Hittorf pointed out, that the result may be accounted for by assuming 
that complex cations are formed by means of which iodine is transferred 
from the anode to the cathode. The effect of this is to lessen the con- 
centration increase of iodine in the neighborhood of the anode due to 
the transfer of the iodide ion. 

If either positive or negative ions of more than one kind occur in 
solution, an equilibrium must exist among them by virtue of which the 
relative concentration of these ions will be a function of the total con- 
centration of the salt. In general, with decrease in concentration, the 
more complex ions break up into simpler ones. It follows, therefore, 
that if complex ions exist in solution, the transference numbers should 
vary as a function of the concentration. 

We may now examine the numerical values of the transference num- 
bers which have been determined for various electrolytes and which are 
given in Table I.^* At a concentration of 5 millimols per liter, the cation 
transference number for sodium chloride, for example, is 0.396. Corre- 
spondingly, the anion transference number is 0.604. This means that in 
a sodium chloride solution of this concentration the fraction 0.396 of 
the current is carried by positively charged carriers, and the remainder 
by negatively charged carriers. It will be observed that, in general, the 

"Hittorf, loo. cit. 

"NoyeB and Falk, J. Am. Chem. 800. SS, 1436 (1911). 



COhDUCTION PROCESS IN ELECTROLYTES 
TABLE I. 



25 



Cation Transpehence Numbers (X 10^) op Various Electrolytes in 
Water at or near 18°. 













Concentration 








Electrolyte 


Temp. 


0.005 0.01 


0.02 


0.05 


0.1 


0.2 


0.3 


0.5 


1.0 


NaCl 


. ... 18° 


396 


396 


396 


395 


393 


390 


388 


382 


369 


KCl 


. ... 18 


496 


496 


496 


496 


495 


494 








LiCl 


. ... 18 


• . . 


332 


328 


320 


313 


304 


9.99 






NH^Cl 


.... 18 


• ■ 


492 


492 


492 












NaBr 


. ... 18 


395 


395 


395 














KBr 


. ... 18 




495 


495 














AgNO, 


. ... 18 


. . , 


471 


471 


471 


471 










HCl 


.... 18 


832 


833 


833 


834 


835 


837 


838 


840 


844 


HNO3 


, ... 20 


839 


840 


841 


844 












BaClj 


. ... 16 


. . . 


. • . 


• • • 




420 


408 


401 


391 




CaCl^ 


. ... 20 


440 


432 


424 


413 


404 


395 


389 






SrCla 


... 20 


. . . 


441 


435 


427 












CdClj, 


, ... 18 


430 


430 


430 


430 


430 










CdBr^ 


...18 


430 


430 


430 


430 


429 


410 


389 


350 


222 


Cdl^ 


...18 


445 


444 


442 


396 


296 


127 


46 


3 




Na^SO, 


...18 


• • ■ 


392 


390 


383 












K^SO, 


...18 


• • • 


494 


492 


490 












TI,SO, 


...25 


• • ■ 


• • • 


• ■ • 


478 


476 










H2SO, 


...20 


• < . 


, , , 


822 


822 


822 


820 


818 


816 


812 


Ba(N03), •■• 


...25 




• • ■ 


■ • • 


456 


456 


456 








Pb(N03), ... 


...25 


> . . 


■ . < 


> > > 


487 


487 










MgSO, 


...18 


388 


385 


381 


373 












CdSO, 


...18 


• • • 


389 


384 


374 


364 


350 


340 


323 


294 


CuSO, 


...18 




. . . 


375 


375 


373 


361 


348 


327 





transference numbers are functions of the concentration. This concen- 
tration effect is much more pronounced in concentrated than in dilute 
solutions, where these numbers appear to approach limiting values. If 
the underlying assumptions are correct and if complex ions are not 
present in solutions of these electrolytes, then the change in the trans- 
ference numbers at higher concentrations indicates a change in the rela- 
tive speed of these ions. In general, at higher concentrations the trans- 
ference number of the more slowly moving ion decreases. A portion of 
the effect at higher concentrations may be due to a transfer of water 
with the ions. But this is not sufficient to account for the entire change 
in the transference numbers. In most cases, the change in the transfer- 
ence numbers does not become pronounced until concentrations are 
reached where the viscosity of the solution is materially affected by the 
electrolyte. Since the motion of a particle through a viscous medium 



26 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

is a function of its viscosity, it may be inferred that in part, at least, 
the variation in the transference numbers at the higher concentrations 
is due to the change of the viscosity of the solution. 

It will be observed that the transference numbers for potassium 
chloride are very nearly 0.5. In other words, in the case of this salt, 
each ion carries very nearly one half of the current. If the frictional 
resistance, which an ion meets in its motion through the medium, is inde- 
pendent of the sign of its charge, then this indicates that the two ions 
have approximately the same dimensions. This is borne out by the 
measurements of Washburn ^°" who showed that these ions are hydrated 
to approximately the same extent. 

The transference numbers of electrolytes are functions of the tem- 
perature. In Table II " are given the transference numbers of a number 

TABLE II. 

Cation Transference Numbers (X 10'') of Various Electrolytes as 
Functions of the Temperature. 



Temp. NaCl KCl HCl BaCl^ 

0° 387 493 845 437 

10 ... 495 841 441 

18 397 496 833 

30 404 498 823 444 

50 ... ... 801 475 

96 ... ... 748 

of electrolytes at temperatures from 0° to 96° at concentrations in the 
neighborhood of 0.015 N. In the case of potassium chloride, the trans- 
ference number varies only very little with the temperature, whereas in 
that of sodium chloride the transference number of the cation increases, 
and in that of hydrochloric acid it decreases. As we shall see later, it is 
a general rule that with increase of temperature the transference numbers 
of all electrolytes approach the value 0.5. The transference numbers of 
ions having values greater than 0.5, therefore, decrease with increasing 
temperature; and those having smaller values increase under the same 
conditions.^ 

3. The Conductance of Electrolytic Solutions. The conductance of 
an electrolytic solution is a function of the various factors which deter- 
mine its condition, such as concentration, temperature, etc. The quan- 
tity actually measured is the specific conductance of the solution. This 
is defined as the conductance in reciprocal ohms of a column of electro- 

'M Washburn, J. Am. Chem. Sob. SI, 322 (1909). 
" Noyes and Falk, loe. cit. 



CONDUCTION PROCESS IN ELECTROLYTES 27 

lyte having a cross-section of 1 sq. cm. and a length of 1 cm. The spe- 
cific conductance is a function of concentration, increasing, in general, 
with increasing concentration. However, in the case of certain electro- 
lytes at very high concentrations, the specific conductance passes through 
a maximum. This is the case, for example, with sulphuric and hydro- 
chloric acids dissolved in water, as well as with certain other electro- 
lytic solutions. 

The specific conductance, however, is a quantity which is not well 
adapted to the purpose of comparing the conductance of different electro- 
lytes. In the case of this property, as in that of many others, it is ad- 
vantageous to refer the numerical values to equivalent amounts of the 
dissolved electrolyte. If, therefore, the conductance of a given electro- 
lyte at two given concentrations is to be compared, the specific con- 
ductance is divided by the equivalent concentration. This quantity is 
called the equivalent conductance. As stated above, the specific con- 
ductance is referred to a unit cube of the electrolyte; that is, to a cube 
having a length of 1 cm. and a cross-section of 1 sq. cm. In order to 
avoid unnecessary factors in the expression for the equivalent con- 
ductance, it is desirable to express the concentration of the electrolyte 
in equivalents per cubic centimeter, rather than in equivalents per liter.^' 
In what follows we shall employ the Greek letter ti to express the con- 
centration in equivalents per c.c, while the letter C will be employed to 
express the concentration in equivalents per liter. We have therefore 
IOOOti = C. If we represent the equivalent conductance by the Greek 
letter A, and the specific conductance by the Greek letter \i, then we 
obviously have: 

Li lOOOu. 

(1) ^=i=-c 

The value of the equivalent conductance A measures, in fact, the 
conducting power of the electrolyte in a solution of a given concentra- 
tion. Suppose, for ex;ample, that one equivalent of electrolyte were con- 
tained between two electrodes 1 cm. wide, separated by 1 cm., and of 
indefinite extent vertically. If the entire electrolyte were contained in 
1 cu. cm. of liquid, then the equivalent conductance would obviously be 
equal to the specific conductance at this concentration, which is unity. 
If, now, more solvent were added to this solution, the amount of solute 
remaining constant, the concentration of the solution would be decreased. 
At the same time there would be an increase in the electrode area, but 
the total amount of conducting material between the electrodes and the 

18 Kohlrauscli and Holborn, "Leitvermogen der Elektrolyte," 1898, p. 84. 



28 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 









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CONDUCTION PROCESS IN ELECTROLYTES 



29 



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30 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

average distance which the conducting particles would have to travel 
between these electrodes would remain fixed. If the cell were filled to a 
height of I centimeters and if the conductance of the solution between 
the pair of electrodes were A, then, since the electrode area is equal to 
the reciprocal of the concentration, i.e., to l/l, it follows that the specific 
conductance of this solution would be: 

[X = -^ = At] 

Therefore, in order to compare the conducting power of a solution of a 
given electrolyte at different concentrations, we divide the specific con- 
ductance of the solution by the concentration and compare the values 
of this ratio, namely the values of A. Similarly, in comparing the con- 
ducting power of solutions of different electrolytes in the same or different 
solvents at the same concentration, the values of the equivalent con- 
ductance of the electrolytes at that concentration are obviously to be 
compared. The equivalent conductance is a measure of the conducting 
of an equivalent amount of material. In comparing the conducting 
power of solutions, therefore, we require the values of the equivalent 
conductance A for these solutions. 

Values of the equivalent conductance of typical electrolytes in water 
at 18° are given in Table III.^® The concentrations in this case are ex- 
pressed in equivalents per liter. It will be observed that as the concen- 
tration of an electrolyte in water decreases, its equivalent conductance 
increases. For a decrease in the concentration in the ratio of one to two 
between normal and half normal, the equivalent conductance of a binary 
electrolyte increases approximately 30%. For a corresponding decrease 
in concentration between 1 and 0.5 milli-equivalent per liter, the equiva- 
lent conductance increases less than 1%. It is apparent, therefore, that 
as the concentration decreases, the equivalent conductance approaches a 
limiting value. 

The relation between the equivalent conductance and the concentra- 
tion is shown graphically in Figure 1, where values of the equivalent 
conductance of aqueous solutions of KCl, NaCl and LilOg are plotted 
as ordinates and the logarithms of the concentrations as abscissas. The 
curves for different electrolytes are evidently similar in form. As the 
concentration decreases, the equivalent conductance apparently ap- 
proaches a definite value as a limit. A curve of this type, however does 
not lend itself to a determination of the limiting value which the con- 
ductance approaches as the concentration decreases indefinitely. For 

•"Noyes and Falk, J. Am. Chem. Soc. Si, 454 (1912). 



CONDUCTION PROCESS IN ELECTROLYTES 



31 



the purposes of graphical extrapolation it is preferable to employ some 
function of the concentration which brings the point of zero concentra- 
tion, to which the extrapolation must be carried, to one of the axes on the 
plot. A convenient function which yields a simple type of curve is the 
cube root of the concentration. Such plots for potassium chloride and 
sodium chloride are shown in Figure 2. If the curves for potassium 
chloride and sodium chloride are extrapolated, they yield for the limit- 
ing value of the equivalent conductance values in the neighborhood of 
130.0 and 108.9 respectively. The value obtained for Ao will, of course, 
depend upon the extrapolation function employed. In another chapter 



3 
T3 

n 
o 
O 



1 




g;s 4.0 4.S 5.0 5.6 2.0 2.e r.o 1.S 0.0 
LogC. 
Fig. 1. Showing A as a Function of Log C for Aqueous Solutions at 18°. 

various functions proposed for this purpose will be discussed more in 
detail. For the present it will be sufficient to employ approximate values 
for the purpose of comparing the behavior of different electrolytes. 

The equivalent conductance of hydrochloric acid is much greater than 
that of the salts. The conductance curve, however, is similar in form 
to that of the salts. That is, with decreasing concentration, the equiva- 
lent conductance approaches a limiting value. In the case of hydro- 
chloric acid this value is in the neighborhood of 380 at 18°. We may 
now ask the question: To what are the differences m the values of the 
equivalent conductance of the different electrolytes due? Why, for ex- 
ample is the equivalent conductance of hydrochloric acid greater than 
that of potassium chloride? Or, in other words, to what is the greater 



32 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

conductance of hydrochloric acid due? It will be recalled that at a 
temperature of 18° and a concentration of 0.01 normal, for example, the 
value of the transference numbers of the positive ions in sodium chlo- 
ride, potassium chloride and hydrochloric acid are 0.396, 0.496 and 
0.833 respectively. In the case of these electrolytes the negative carrier 



130 
120 














\ 


















< 






\v /fC/ 






inductance 






\^ 








\ 


^ 


-\ 




Equivalent Cc 

§ 8 




\ 






^^"*v^ 






\w«a 










\ 


^ 




eo 

70 








^\ 












"\ 



O.O 0.Z 0.4- 0.6 0.& 

Cube Root of Concentration, C%. 

Fig. 2. Showing A as a Function of C^. 



1.0 



is presumably the same, namely, the chloride ion, and it is only the posi- 
tive carriers which differ in these electrolytes. If, then, the negative 
carriers are the same in solutions of these electrolytes, it may be assumed 
that the current carried by these carriers in these solutions under the 
same conditions of temperature and concentration will be approximately 
the same, and consequently the difference in the conducting power of 
these electrolytes is due to the difference in the conducting power of 
their positive carriers. The carrying capacities of the sodium, potassium 



CONDUCTION PROCESS IN ELECTROLYTES 33 

and the hydrogen ions are, therefore, 0.656, 0.984 and 1.972 times that 
of the chloride ion respectively. In other words, the carrying capacity 
of the hydrogen ion is 3 times that of the sodium ion and 2 times that 
of the potassium ion. If the tables of the conductance and of the trans- 
ference numbers are compared, it will be seen that in the more dilute 
solutions it is generally true that, for salts having an ion in common, 
those salts whose ions have greater transference numbers likewise have 
greater conducting power. 

We now come to an important generalization due to Kohlrausch,^" 
namely: In a solution of a single electrolyte, the two ions move inde- 
pendently of each other. Therefore, we may determine the fraction of the 
current carried by each ion, or, in other words, the conductance of each 
ion in a given solution, by multiplying the equivalent conductance of 
the solution by the transference number of the electrolyte in this solu- 
tion. If this is true, then, in a solution of sodium chloride having a 
concentration of 0.01 normal at 18°, the conductance due to the sodium 
ion is 101.88 X 0.396 =A-j^g^= 40.34. Similarly, the conductance of the 

potassium and hydrogen ions under the same conditions is: 

Aj^ = 122.37 X 0.496 = 60.69 

and Ajj = 369.3 X 0.833 = 307.63 

In these solutions the conductance of the chloride ion is 61.54, 61.68 and 
61.67 for NaCl, KCl and HCl respectively. The conductance of the 
chloride ion is thus very nearly the same in equivalent solutions of these 
electrolytes. It is, however, by no means certain that the conductance 
of a given ion will in all cases be the same in solutions of different salts. 
If the transference numbers of an electrolyte are known at a given con- 
centration, then the conductance of its ions may be calculated. 

4. Ionization of Electrolytes. As we have seen, the equivalent con- 
ductance of a solution, which measures, so to speak, the conducting 
power of the dissolved electrolyte under given conditions, increases with 
decreasing concentration and appears to approach a limiting value. The 
current passing through an electrolyte under given conditions is carried, 
in the case of the simpler types of salts, by two charged constituents, 
namely the positive and the negative carriers, which, according to Fara- 
day, are termed the cation and the anion respectively. The relative 
amounts of the current carried by the positive and negative ions may 
be determined by means of transference experiments, which depend ulti- 
mately upon the concentration changes produced by the motion of the 

2»Gottinger, "Nachrichten," 1876, p. 213. 



34 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

carriers. If the current in a solution of an electrolyte is effected through 
the motion of charged carriers within the electrolyte, then we may in- 
quire: What fraction of the electrolyte present in the solution is con- 
cerned in the process of conduction; that is, what fraction of the electro- 
lyte exists in an ionic condition? ^ 

Clausius ^^ suggested that electrolytes are ionized, but he failed to 
draw any definite conclusion as to the extent of this ionization. In his 
time, the notion that a stable compound, such as potassium chloride, 
could be dissociated and moreover dissociated into oppositely charged 
constituents was contrary to accepted theories. Clausius was therefore 
content to merely throw out the suggestion that electrolytes are to some 
extent dissociated. 

The conclusion that an electrolyte is dissociated follows almost neces- 
sarily from the work of Kohlrausch and Hittorf, although neither of 
these investigators actually drew this conclusion. It was Arrhenius '"' 
who proposed the fundamental hypothesis that an electrolyte in solution 
is dissociated and that the degree of its dissociation may be determined 
by means of the conductance of its solutions. Moreover, he showed that 
the dissociation as measured in this way is in agreement with many 
other well-known properties of these solutions. 

We have seen that, as the concentration of a solution decreases, its 
equivalent conductance increases and approaches a limiting value. We 
have also seen that the positive and negative ions within the electrolyte 
appear to move at definite rates under fixed conditions, provided the con- 
centration of the solution is not too great, and that the motion of the 
ions under these conditions takes place independently for each ion. If 
these conclusions are correct, then it appears that a logical explanation of 
the facts would be that, in the more concentrated solutions, a portion of 
the electrolyte has been removed from a condition in which it is able 
to take part in the conduction process, while the fraction of the sub- 
stance which remains in a conducting condition is measured by the ratio 
of the conductance at a given concentration to the conductance at very 
low concentrations, where apparently all the electrolyte takes part in the 
conduction process. 

Let Y represent the fraction of the salt present in a conducting state; 
then the relative amount of the salt present in this state at any con- 
centration will be given by the ratio: 

(.. v = A, 

"Clausius, Pogg. Ann. 101, 338 (1857). 

"Arrhenius, Bijhanj till K. Svenaka, Vet. Akad. Handl. No. 18. 1884- Sixth r^miigii 
of the British Association Corotnittee tor Electrolysis, May, 1887 ; Ztsehr. f.phya^ Che", 
it 631 (1887) » 



CONDUCTION PROCESS IN ELECTROLYTES 



35 



where A is the equivalent conductance of the solution at the concentra- 
tion C, and Ao is the limiting value which the conductance approaches 
as the concentration decreases without limit. According to this theory, 
we may calculate the fraction of electrolyte in an ionized condition, if 
we know the equivalent conductance and the limiting value which the 
equivalent conductance approaches at zero concentration. In Table III 
were given values of the equivalent conductance of a number of electro- 
lytes at a series of concentrations. The approximate limiting values 
Ao, which the equivalent conductance approaches at low concentrations, 
appear in the second column of that table. From these values we may 
calculate the degree of ionization of the electrolytes at any concentration 
falling within the intervals given. In the case of potassium chloride, 
for example, Ao = 130.0, approximately, and the equivalent conductance 
at normal concentration is 98.22. Therefore, the ionization of potassium 
chloride at this concentration is approximately 75%; that is, of the total 
potassium chloride present in solution at this concentration, 75% is con- 
cerned in the actual process of conduction and 25% takes no part in this 
process. 

The ionization values of various electrolytes in water at 18° are given 
in Table IV.^^ It will be observed that the ionization of salts of the 

TABLE IV. 

Ionization Values of Electrolytes in Water at 18°. 



Concentra- 
tion, C. 

NaCl .... 

KCl 

LiCl 

RbCl .... 

CsCl 

TlCl 

KBr 

KI 

KSCN ... 

KF 

NaF 

TIF 

NaNO, ... 



10-^2 

.977 

.979 

.975 

.980 

.978 

.976 

.978 

.978 

.978 

.978 

.974 



X 10-" 
.969 
.971 
.966 

!969 
.965 
.970 
.970 
.970 
.970 
.964 



.977 .968 



5 X 10- 
.953 
.956 
.949 

!954 
.942 
.955 
.956 
.955 
.954 
.945 
.961 
.950 



'10-' 
.936 
.941 
.932 
.942 
.937 
.915 
.940 
.941 
.940 
.937 
.925 
.936 
.932 



X 10-= 


5 X 10- 


10-' 2 X 10-' 


5 X 10- 


M.O 


.916 


.882 


852 


.818 


.773 


.741 


.922 


.889 


860 


.827 


.779 


.742 


.911 


.878 


846 
855 
847 


.812 


.766 


.737 

.748 


!92i 


!888 


859 


!825 


!766 


.... 


.922 


.890 


869 


■ • < . 


.773 


.727 


.920 


.888 


860 


. • ■ . 


. . • . 


.■ ■ . 


.915 


.878 


> • ■ 


• • • ■ 


* ■ • . 


• • ■ ■ 


.899 


.854 


• > • 


.... 


.. • . 


• ■ • • 


.908 


.865 


. > . 


.... 


.... 


■ > • . 


.910 


.871 


832 


.788 


.719 


.660 



Noyes and Falk have cor- 
While there 



« Noyes and Falk, J. Am. Chem. Soc. 3J,, 454 (1912). 

In calculating the ionization at the higher concentration ^ , , , , 
rected for the viscosity change of the solution due to the added electrolyte 
Is e^ry reason for believing that the change in the viscosity ot the solution entails a 
change tattf speed of the ca^rriers, in general the change ^JPf^ is probably not directly 
proportional to the change in the fluidity of the medium. /", ™'^^t'°P„^^'{L^\|* ?f ^?' 
concentrations, therefore, are more or less in doubt As a. rule the viscosity ettects are 
small at concentrations below 10"' N. In comparing the ionization of ^"O"^!'"'*^"'^'-^?' 
tberefore, it is best to choose concentrations at which the viscosity effect may be neglected. 



36 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



TABLE IV.— Continued 



Concentra- 
tion, C. 

KNO3 

LiNO, .... 

TINO3 .... 

AgN03 . . ; . 

KBrOa .... 
KCIO3 .... 
NalOg .... 

KIO3 

LilOj 

HCl 

HNO3 

BaCl^ 

CaCl3 

MgCU .... 

PbCl^ 

CdCl, 

CdBr^ 

Cdl^ 

Ba(N03)2 . 
Sr(N03), .. 
Ca(N03)/. 
Mg(N03),. 
Pb(N03), . 
Cd(N03), . 
Ba(Br03)2.. 

K,SO, 

Na^SO, .... 

LiSO^ 

T1,S0, .... 
Ag^SO, .... 
K2C2O1 . . . 
MgSO^ .... 

ZnSO, 

CdSO^ .... 
CuSO, .... 
MgC.O, . . . 
K,Fe(CN)e. 

La(N03)3 . 
K3C8H5O7 . 

La, (SO J 3 . 
Ca2Fe(CN)„ 



10-'2 X 10-' 

.978 .970 

.975 .965 

.977 .967 

.977 .968 

.980 .970 

.978 .969 

.971 .960 

.975 .965 

.970 .958 

.990 .988 

.992 .987 

.956 .... 

.954 .938 

.955 .939 

.943 .917 

.931 .891 

.897 .858 

.870 .809 

.953 .934 

.953 .935 

.954 .937 

.953 .936 

.947 .926 

.996 .974 

.947 .927 

.954 .937 

.939 .925 

.946 .... 

.948 .924 

.949 .927 

.960 .945 

.873 .823 

.854 .799 

.850 .791 

.862 .804 

.582 .472 

859 

902 

926 

464 

514 



5x 10- 
.953 
.950 
.948 
.950 
.954 
.952 
.939 
.946 
.936 
.981 



.910 
.910 
.865 
.803 
.749 
.675 
.898 
.904" 
.907 
.907 
.886 
.917 
.892 
.905 
.893 

^882 
.885 
.916 
.740 
.710 
.694 
.709 
.350 



.882 



10-=^ 2 

.935 

.932 

.926 

.931 

.934 

.933 

.917 

.928 

.912 

.972 

.970 

.883 

.882 

.883 

.808 

.735 

.661 

.573 

.861 

.871 

.876 

.880 

.845 

.871 

.856 

.872 

.857 

.854 

.837 

.840 

.886 

.669 

.633 

.614 

.629 



X 10-' 

.911 

.911 

igos 

.910 
.910 
.890 
.903 
.883 
.962 

.856 
.849 
.851 
.738 
.664 
.573 
.469 
.818 
.833 
.838 
.847 
.793 
.848 
.812 
.832 

^sii 

.780 
.784 
.849 
.596 
.556 
.534 
.550 



5 X 10 

.867 

.874 

.843 

.859 

.868 

.866 

.842 

.860 

.834 

.944 

.940 

.798 

.802 

.803 

.627 

.559 



^ 10-^ 2 

.824 

.840 

.788 

.814 

.830 

.827 

.801 

.819 

.789 

.925 

.921 

.759 

.764 

.765 



X 10-' 

.772 

.803 



.780 
.752 

.775 
.740 



.720 

.727 
.728 



5 X 10-' 1.0 
.688 .613 
.750 .703 

!683 .617 

703 .... 

!682 .643 



.672 .642 
.686 .662 
.687 .669 



.453 .375 .289 .217 



.744 .679 

.770 .719 

.781 .731 

.799 .760 

.708 .635 

.792 .731 



.609 .504 .... 

.661 .579 .511 

.679 .609 .549 

.721 

.559 .454 .377 

.684 .628 .577 



.771 .722 

.756 .704 

.744 .688 

.694 .625 



.673 
.652 
.633 
.561 



618 .592 
567 !528 



.795 .753 

.506 .449 

.464 .405 

.437 .377 

.455 .396 



.711 
.403 
.360 
.332 
.351 



.712 
.802 
.817 
.289 
.339 



.591 .538 .498 

.701 

.705 

.198 

.262 



. .643 

, .349 

. .309 

,290 .277 

. .309 



same type is approximately the same at the same concentration. This 
is particularly true at the lower concentrations where the divergence in 
many cases is scarcely greater than the experimental error. The strong. 



CONDUCTION PROCESS IN ELECTROLYTES 37 

acids and bases, however, have a markedly higher ionization than the 
salts. Salts of higher type exhibit a lower degree of ionization than 
simpler salts. But here, again, salts of the same type have approxi- 
mately the same ionization at corresponding concentrations. 

If electrolytes approach complete ionization at low concentrations 
and if the ions in these solutions move independently of one another, 
then, if the transference numbers of the electrolytes are known, the value 
of the equivalent conductance of the individual ions may be calculated. 
If the conductances of a sufficient number of pairs of electrolytes have 
been determined, it is only necessary to know the transference number 
of a single electrolyte. In general, the values of the ionic conductances 
are based upon the transference number of potassium chloride. The 
values of the equivalent conductances of various ions in water at 18° are 
given in Table V.^* 

TABLE V. 

EomvALENT Conductances of the Individual Ions at 18°. 

Cs 68.0 Ba 55.4 CI 65.5 

Rb 67.5 Ca 51.9 NO3 61.8 

Tl 65.9 Sr 51.9 SCN 56.7 

NH, 64.7 Zn 47.0 CIO3 55.1 

K 64.5 Cd 46.4 BrOg 47.6 

Ag 54.0 Mg 45.9 F 46.7 

Na ,.... 43.4 Cu 45.9 IO3 34.0 

Li 33.3' La 61.0 SO, 68.5 

H 314.5 Br 67.7 CA 63.0 

Pb 60.8 I 66.6 Fe(CN)„ 95.0 

The equivalent conductance values of the different ions are of the 
same order of magnitude, although the values for the hydrogen and 
hydroxyl ions are markedly greater than for the other ions. This is in 
agreement with the greater values of the conductance of solutions of 
the strong acids and bases. The conductance values of the different ions 
appear to bear no simple relation to their constitution. So, for ex- 
ample, lithium, which is lighter and has a smaller atomic volume than 
the remaining alkali metals, has the lowest conductance of any of the 
ions whose conductance values are tabulated. On the other hand, the 
nitrate and the chloride ions have markedly higher values than the 

fluoride ion. rr^, , .1 • r 

5 Molecular Weight of Electrolytes in Solution. The hypothesis of 

Arrhenius, that the ionization of an electrolyte may be measured by the 

"Noyes and Falk, loc. cit. 



38 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ratio of the equivalent conductance at any concentration to the limiting 
value of the equivalent conductance at low concentrations, is supported 
by other important properties of these solutions. Raoult ^^ had observed 
that the freezing point depression produced by electrolytes in water is 
greater than that of other substances at equivalent concentrations, van't 
Hoff,^° finally, supplied the theoretical foundation which made it pos- 
sible to calculate from the measurements of Raoult the molecular weight 
of substances in solution. Since in the case of aqueous salt solutions the 
depression was found to be abnormal, van't Hoff introduced an arbitrary 
factor i, which he apparently assumed to be a constant independent of 
concentration. Arrhenius at once recognized the significance of van't 
Hoff's factor and pointed out the relation between this factor and the 
coefficients derived from conductance measurements. According to 
Arrhenius, if electrolytes are dissociated, the freezing point depression of 
their solutions as measured should be greater than that calculated ac- 
cording to the method of van't Hoff, the molecular weight being assumed 
equal to the formula weight of the dissolved substance. If we let 

where M is the formula weight and Mq the molecular weight calculated 

from freezing point measurements, then, obviously, there exists between 
i and y, the relation: 

(4) i=l+{n—l)y, 

where n is the number of ions resulting from the dissociation of a single 
molecule. The values of y as calculated from freezing point or other 
similar determinations should thus agree with the values of y as calcu- 
lated from conductance measurements. In Table VI ^' are given the 

TABLE VI. 

Comparison of Ionization Values Derived from Conductance and 
FROM Freezing Point Measurements. 

Electrolyte Method 5 X 10-* 10-= 2 X 10-' 5 X 10-' 10-' 2 X 10-' 5 X 10-' 

KCl F .963 .943 .918 .885 .861 .833 .800 

C .956 .941 .922 .889 .860 .827 779 

NH.Cl F .947 .928 .907 .878 .856 832 

C 941 .921 , ;... 

"O. B. 9i, 1517; 95, 188 and 1030 (1882). 

"van't Hoflf, Sv. Yet.-Akad. Handlingar 21, No. 17 (1886), p 48 

"Noyes and Falk, J. Am. Chem. 8oo. Si, 485 (1912). The concentrated soluMons 
have been corrected for the viscosity effects. (See fiotnotc above, p 35.) ^<"""»°^ 



CONDUCTION PROCESS IN ELECTROLYTES 39 



TABLE VI.- 

Electrolyte Method 5X10-' 10-" 

NaCl F .953 .938 

C .953 .936 

CsCl F 

C .954 .937 

LiCl F .944 .937 

C .949 .932 

KBr F 

C .955 .940 

NaNOs F 903 

C .950 .932 

KNO3 F 901 

C .953 .935 

KCIO3 F 914 

C .952 .933 

KBrOg F 923 

C .954 .934 

KIO3 F .941 .913 

C .946 .928 

NalOg F .939 .916 

C .939 .917 

KMnO^ F .938 .921 

C .968 .951 

HCl F .991 .975 

C .981 .972 

HNO3 F .974 .960 

C 970 

Bad, F .899 .878 

C 883 

CaCL F 

C .910 .882 

MgCla F 

C .910 .883 

CdCl, F 791 

C .803 .735 

CdBr, F 780 

C .749 .661 

Cdl, F 593 

C .675 .573 

Cd(N03)2 F .948 .921 

C .917 .871 

Ba(N03), F .917 .888 

C .898 .861 

Pb(N03)2 F .890 .850 

C .886 .845 

K,SO, F .929 .899 

C .905 .872 



-Continued 






2X10-= 


5X10-" 


10-" 


2X10-' 5x1 


.922 


.892 


.875 


.850 .8! 


.916 


.882 


.852 


.818 .7' 


.930 


.892 


.863 

.847 


.829 .7 


.928 


.912 


.901 





.890 


.878 


.846 


.812 .7 


.929 


.889 


.863 


.839 .8 


.921 


.888 


.859 


.825 ,7 


.885 


.855 


.830 


.798 .. 


.910 


.871 


.832 


.788 .7 


.880 


.836 


.781 


.711 .. 


.911 


.867 


.824 


.772 .6 


.891 


.849 


.798 


• • • ■ ■• 


.910 


.866 


.827 


.780 .7 


.896 


.854 


.805 


• • • • •• 


.910 


.868 


• • ■ • 


• • • • •• 


.882 


.828 


.765 





.903 


.860 


.819 


.775 ., 


.890 


.842 


.773 





.890 


.842 


.801 


.752 '.. 


.913 


,, , , 


• • • • 


• • • • • • 


.930 


• ■ • • 


■ • • • 


• ■ • • • • 


.957 


.933 


.917 


«• • • •• 


.962 


.944 


• • • • 


• • • • •• 


.942 


.912 


.900 


.879 . 


• • • • 


.940 




• • • • • • 


.855 


.819 


.788 


.758 .. 


.850 


.798 


.759 


.720 .6 


.876 


.837 


.815 


.804 .. 


.849 


.802 


.764 


.727 .6 


.885 


.854 


.839 


.833 .. 


.851 


.803 


.765 


.728 .6 


.768 


.690 


.605 


.539 .. 


.664 


.559 


.453 


.375 .2 


.704 


.589 


.482 


.367 .. 


.573 


• • ■ > 


• • • • 


• • • • •• 


.540 


.400 


.225 


.100 .. 


.469 


■ • • • 


■ • • • 


■• • • •• 


.901 


.887 


.884 





.848 


.792 


.731 


.684 .6 


.855 


■ • • • 


• • • • 


• • • • •• 


.818 


.744 


.679 


.609 .5 


.804 


.724 


.649 


.568 A 


.793 


.708 


.635 


.559 .4 


.857 


.785 


.730 


.667 .5 


.832 


.771 


.722 


.673 .6 



40 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



TABLE VI.- 

Electrolyte Method 5x10-' 10-=' 

Na^SO^ F 

C .893 .857 

MgSO, F .694 .618 

C .740 .669 

CuSO, F .616 .545 

C .709 .629 

ZnSO, F .665 .582 

C .710 .633 

CdSO^ F .658 .569 

C .694 .614 

K3Fe(CN)e F .894 .868 

C .869 .827 

K,Fe(CN)e F 

C 



-Continued 
2X10-" 5X10- 



867 

536 
596 
455 
550 
489 
556 
477 
534 
778 



.795 
.756 
.420 
.506 
.318 
.455 

!464 
.343 
.437 



.634 
.591 



10-' 


2X10-' 


5X10-' 


.736 
.704 
.324 
.449 


.672 
.652 
.223 
.403 


.567 


!396 


!35i 




'Jm 


!366 


• • • • 


'.2,-11 


!332 


.290 


!58i 
.538 


^520 
.498 


.425 

• • • • 



values of y as determined from freezing point (F) and from conductivity 
(C) measurements. 

It will be observed that in the case of certain electrolytes the values 
of Y derived by the two methods correspond very closely. This is par- 
ticularly true of potassium chloride where the two values correspond 
practically within the limit of experimental error up to concentrations as 
high as 0.1 normal. In the case of other salts, the divergence at higher 
concentrations is considerably greater. In general, however, the two 
values approach each other the more nearly, the lower the concentration 
of the solution. The correspondence between the two values is closest 
in the case of the binary salts. The more complex a salt, the greater is, 
as a rule, the divergence between the two values and the lower the con- 
centration at which a given divergence appears. 

The cause of the divergence of the ionization values as determined 
by the two methods is as yet uncertain. It is possible that the ionization 
is not correctly measured by the conductance ratio. At higher concen- 
trations, at any rate, it is to be expected that various influences will make 
themselves felt, such as the effect of viscosity, as a result of which the 
conductance as measured will not yield a true measure of the ionization. 
On the other hand, the molecular weight, as determined by osmotic 
methods, may be expected to be in error, since the laws of dilute solu- 
tions are assumed in calculating these values. The only assurance we 
have that the laws of dilute solutions are applicable under given condi- 
tions is that the results obtained are in agreement with other facts re- 
lating to these solutions. When a disagreement occurs, therefore it is 



CONDUCTION PROCESS IN ELECTROLYTES 41 

not known whether the laws of dilute solutions are inapplicable or 
whether some other discrepancy has arisen. 

In the case of salts of higher type, and even in that of the simpler 
types of salts, there is always a possibility that the ionization process as 
assumed in calculating the ionization from conductance measurements 
does not correspond to the true reaction. For example, in calculating the 
ionization of barium chloride, it is assumed that the reaction takes place 
according to the equation: 

BaOl^ = Ba++ + 201". 

It is possible, however, that ionization may take place in several stages, 
an intermediate reaction of the type: 

BaCl^ = BaCl^ + Ch 

intervening. If an intermediate reaction of this type takes place, then 
it is obviously impossible to calculate the degree of ionization from con- 
ductance measurements. So far, it has proved difficult to establish the 
existence of intermediate ions. In general, it is to be expected that if 
intermediate ions exist, the transference numbers will vary markedly 
with the concentration. It should be noticed in this connection that 
those electrolytes, which exhibit the greatest divergence between the 
ionization values as calculated from conductance and from freezing point 
data, also exhibit a marked change in their transference numbers with 
change of concentration. In the case of sulphuric acid ^^ the existence of 
an intermediate ion has been definitely established; and various consid- 
erations, based upon the solubility of salts in the presence of other salts, 
lend support to the view that intermediate ions exist in solutions of 
many salts of higher type.^' 

In any case, it is important to note that the values of i as deter- 
mined from freezing point and from conductivity determinations appar- 
ently approach the same limit at low concentrations, and, moreover, the 
limits approached are in agreement with the constitution of the salts in 
question. So, for example, in the case of the binary electrolytes, the 
limit approached is 2, in that of ternary electrolytes 3, in that of quater- 
nary salts 4, etc. No case has been observed in which the limit ap- 
proached is greater than that corresponding to the constitution of the 

salt. 

6. Applicability of the Law of Mass Action to Electrolytic Solutions. 
On their surface, the results of conductance and of freezing point meas- 
urements appear to be in substantial agreement with the fundamental 

M Noyes and Eastman, Carnegie Report No. 19, p. 241. 
s'Harklns, J. Am. Ohem. Sac. SS. 1808 (1911). 



42 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

hypothesis of Arrhenius; namely, that an electrolyte in solution is ion- 
ized, and its ionization is a function of the concentration, decreasing with 
increasing concentration. There exists, therefore, in solutions of electro- 
lytes an equilibrium between the ions and the un-ionized molecules, and 
this equilibrium must be subject to the usual laws governing equilibria. 
It is obvious that, according to the law of mass action, the ionization 
should increase with decreasing concentrations, since there is an increase 
in the number of molecular species as a result of the reaction. If we 
assume a simple system, as for example a binary salt MX which forms 
the ions M* and X", according to the equation: 

MX = M* + X-, 

then, according to the law of mass action, we should have a relation: 

Cm+-^ ^x- 

(5) -^ — = K, 

^MX 

where C^ represents the concentration of the molecular species X. If 

the solution is sufi&ciently dilute, so that the laws of dilute solutions may 
be' applied, then K will be a function of the temperature only. On the 
other hand, it is obvious that a concentration must ultimately be reached 
where the laws of dilute solutions fail, in which case K becomes a func- 
tion of the concentration as well as of the temperature.^" 

If Y is the degree of ionization of the salt and if C is its total concen- 
tration, then the concentrations of the two ions will be equal to Cy and 
the concentration of the un-ionized fraction will be equal to C(l — y). If 
these values are substituted in Equation (5), they lead to the equation: 

(6) ^=K. 

1 — Y 

The value of y may be calculated either from conductance or from 
osmotic measurements. If the values of y according to the two methods 
agree, then obviously the two methods must lead to identical results, so 
far as the mass-action law is concerned. Since the degree of ionization 
is given by Equation 2, we may substitute this value of y in Equation 6 
which yields the equation: 

This equation, involving the two constants K and Ao, therefore expresses 
the relation between the concentration and the conductance of a solution 

"»Van der Waala-Kohnstamm, "Lehrbuch der Thermodynamlk," part 2, pp. 604 



CONDUCTION PROCESS IN ELECTROLYTES 43 

of a binary electrolyte. In general, to test the applicability of this 
equation, the value of A„ must first be determined by some method of 
extrapolation, after which the constancy of the function K may be 
determined by substituting in the above equation. In Table VII ^^ are 

TABLE VII. 
Values of K for Acetic Acid in Water at 25°. 

y A ii: X 100 



0.989 


1.443 


0.001405 


1.977 


2.211 


0.001652 


3.954 


3.221 


0.001759 


7.908 


4.618 


0.001814 


15.816 


6.561 


0.001841 


31.63 


9.260 


0.001846 


63.26 


13.03 


0.001846 


126.52 


18.30 


0.001847 


253.04 


25.60 


0.001843 


506.1 


35.67 


0.001841 


1012.2 


49.50 


0.001844 


2024.4 


68.22 


0.001853 



0= 387.9 — 

given values for the conductance of acetic acid in water at 25° at a 
series of concentrations. In this table, V denotes the dilution in liters 
per equivalent, A the equivalent conductance and K the ionization con- 
stant, calculated according to Equation 7. 

It will be seen that at higher concentrations, down to about 0.1 nor- 
mal, there is a marked change in the value of the function K, but at 
concentrations below 0.1 normal the function K remains constant, prac- 
tically within the limits of experimental error.^^" At the highest dilution 
in the table the function K shows a slight increase, which is probably 
due to a discrepancy between the experimental values and the assumed 
value of Aq. In general, the weaker the acid, the greater the range of 
concentration over which the function K remains constant. In other 
words, the concentration, at which the function K varies measurably 
from constancy, increases as the strength of the acid increases. In Table 
VIII ^^ are given values of the equivalent conductance and the ionization 
constant of trichlorobutyric acid at a series of concentrations. It will be 

"Kendan, Med. Veten. Akad. Noieliiistitut 2, No. 38, p. 1 (1913). 

sia Tiie decrease in tbe value of K at higher concentrations is in part, if not largely, 
due to the increasing viscosity of the solution. Compare Washburn, "Principles of Physi- 
cal Chemistry," 2nd Ed., p. 340. 

"Kendall, loo. cit. 



44 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE VIII. 
• Values of K foh Teichloeobutyhic Acid in Water at 25°. 
V A if X 100 



5.90 


237.3 


18.3 


11.80 


276.8 


17.4 


23.59 


308.5 


15.9 


38.63 


326.4 


14.8 


47.18 


331.8 


14.0 


53.98 


336.0 


13.9 


77.26 


343.9 


12.7 


107.96 


350.4 


11.8 


154.5 


357.0 


11.5 


215.9 


361.2 


10.9 


309.0 


365.1 


10.5 


431.8 


368.2 


10.7 



618.0 370.9 (11.6) 

00 376.0 — 

observed that the function K decreases throughout as the concentration 
decreases, but that the decrease is more marked at higher concentrations 
and that, apparently, at lower concentrations a limiting value is ap- 
proached. The slight variation in the value of K at the lowest con- 
centrations may be due either to experimental errors or to a discrepancy 
in the value of Ao. In general, we may say that electrolytes, such as 
acetic acid, fulfill the condition that in the more dilute solutions the 
function K remains substantially constant. The same holds true in the 
case of the weak bases. 

Obviously, these results afford strong confirmative evidence of the 
correctness of the fundamental assumption that these electrolytes are 
ionized in' solution according to a reaction equation of the following type: 

CH3COOH = CH3COO- + H^ 



On the other hand, when we proceed to a consideration of typical'salts^ 
or what are commonly known as strong electrolytes, we find that K ap- 
pears throughout to be a function of the concentration, its value decreas- 
ing as the concentration decreases. 

Below are given the values of the function K at a series of concen- 
trations for solutions of potassium chloride in water at 18° : '* 

•• The manner In which K varies with the concentration at very low concentrations 
is uncertain, since small errors in the extrapolated value of A„ cause a large variation 
lu the resulting value of the function K. The values here given are based on the valno nf 
A„ derived by the author. J. Am. Ohem. Soo. J,Z, 1 (1920). Compare, also, Wetland i6id 
Jfi, 146 (1918] • * *' 



CONDUCTION PROCESS IN ELECTROLYTES 45 

TABLE IX. 

Valxtes of K for KCl in Water at 18°. 

C= 10'* 10* 10'' 10-^ 10-^ 1.0 

X = . 00518 .0147 .0474 .1542 .5052 2.14 

It will be observed that in this case the function K decreases enormously 
with decreasing concentration. Whether the function approaches a finite 
limit, or whether it approaches a limit zero at low concentrations, cannot 
be determined with certainty. In general, the stronger the electrolyte, 
the more does the function K vary with the concentration and the 
greater is its value at a given concentration. In the case of hydrochloric 
acid the values of X at a number of concentrations are as follows: 

TABLE X. 

Values of K for HCl in Water at 18°. 

■ C= 10-=" 10-= 10-^ 

K = 0.189 0.366 1.11 

If these values are compared with those for potassium chloride, it will be 
seen that the value of K is considerably greater for hydrochloric acid 
than it is for potassium chloride. At 0.1 normal the value of K for 
hydrochloric acid is approximately twice that for potassium chloride. 
In the more dilute solutions, however, this ratio appears to increase, since 
in a 0.001 normal solution the value for hydrochloric acid is approxi- 
mately four times that of potassium chloride. 

In view of the fact that electrolytes of a given type appear to be 
ionized to practically the same extent in water, it follows that the dis- 
crepancies found for different electrolytes of the same type will be of 
the same order of magnitude. 



Chapter III. 

The Conductance of Electrolytic Solutions in Various 

Solvents. 

1. Characteristic Forms of the Conductance-Concentration Curve. 
The property of forming solutions which possess the power of con- 
ducting the current is one not restricted to water. Nor, indeed, are 
electrolytes in non- aqueous solvents restricted entirely to those sub- 
stances which are electrolytes in aqueous solution. As the field of non- 
aqueous solutions has been extended in recent years, it has become more 
and more apparent that the property of forming solutions which conduct 
the current is one which is common to a great many substances. Indeed, 
it seems not improbable that all liquid non-metallic media yield elec- 
trolytic solutions when suitable substances are dissolved in them. 

In attempting to account for the properties of electrolytic solutions in 
water, it is difficult to distinguish between those properties which are 
characteristic of electrolytic solutions in general and those which are 
characteristic of aqueous solutions alone. Such a knowledge can be 
obtained only from a study of the properties of electrolytic solutions in a 
large variety of solvents, and it appears unlikely that the properties of 
electrolytic solutions may be successfully accounted for until we possess 
reliable data as to the properties of non-aqueous solutions. While this 
field has been greatly extended during the past two decades, it is only in 
the case of a few solvents that we possess a suflacient mass of facts to 
enable us to treat the subject with a measurable degree of completeness. 

From a constitutional point of view, the alcohols are more nearly 
related to water than are any other solvents, since they may be looked 
upon as water in which one of the hydrogen atoms has been substituted 
by a hydrocarbon group. We should expect the properties of these 
solvents to diverge progressively from those of water as the size and 
complexity of the hydrocarbon group increases, and such has indeed been 
found to be the case. In general, the ionizing power of the alcohols 
diminishes as the complexity of the carbon group increases. Accord- 
ingly, methyl alcohol stands much nearer to water than do any of the 
other representatives of this class of solvents. 

For the purposes of illustration we may consider the conductance of 

46 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 47 

sodium iodide in ethyl alcohol, the values of which are given in Table 
XI: ^ 

TABLE XI. 

Conductance of Sodium Iodide in Ethyl Alcohol at 18°. 

V 125 250 500 1000 2000 4000 8000 oo 

A 28.6 31.3 33.5 35.2 36.5 37.6 38.3 39.4 

Y 0.726 0.794 0.850 0.894 0.926 0.954 0.972 1.0 

It will be observed that the conductance of solutions in ethyl alcohol 
increases with decreasing concentration in a manner similar to that 
of solutions in water. The limiting value of the equivalent conductance, 
that is the value of Ao, for a solution of sodium iodide in ethyl alcohol 
is in the neighborhood of 39.4. It follows, therefore, that the ionization 
values of solutions in ethyl alcohol are considerably smaller than those 
of solutions in water. In Figure 3, the ionization of sodium iodide in 
ethyl alcohol is shown as a function of concentration. In the same figure, 
the ionization of sodium chloride in water is likewise shown. 

Acetone is another solvent whose solutions resemble those in water 
in many respects. The conductance of sodium iodide in acetone at 18° 
at a series of concentrations is given in Table XII: ^ 

TABLE XII. 
Conductance of Sodium Iodide in Acetone at 18°. 



V .. 


.. 292.6 


1030 


4083 


8874 


18660 


39700 


64827 


00 


A .. 


.. 112.8 


131.1 


147.7 


151.0 


154.8 


155.2 


156.0 ? 


156.0 


Y •• 


. . 0.723 


0.841 


0.947 


0.968 


0.992 


0.995 


— 


— 



Here, again, it will be observed that the equivalent conductance rises 
throughout with decreasing concentration. While the conductance values 
of acetone solutions are greater than those of solutions in ethyl alcohol, 
the degree of ionization is very nearly the same in the two solvents. In 
both ethyl alcohol and acetone the ionization is much lower than it is in 

water. 

Another typical solvent is found in liquid sulphur dioxide. The con- 
ductance values of solutions of potassium iodide in sulphur dioxide at 
— 33° and at — 10° are given in Table XIII: ^ 

iDutoit and Eappeport, Jour. d. Chim.-Phus. 6, 5i5il90S-). 
^Dutoit and Levrier, Jour. d. Chtm.-Phya. 3, 43 (1905), 
•Franklin, J. PJiys. Cliem. IS, 675 (1911), 



48 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 
1.00 




0.0 



3.0 



4.0 



1.0 2.0 

Log V. 

FiQ. 3. Ionization of Binary Electrolytes in Different Solvents. 









TABLE XIII. 












Conductance of KI in SOj at — 33° 


and — 


10°. 




V 




. 0.50 1.00 


2.0 4.0 8.0 


16.0 


32.0 


64.0 


A_ 


-33° 
-10° 


.. 27.5 37.7 
.. 39.7 46.9 


40.1 40.5 41.0 
46.8 44.8 42.5 


42.7 
43.5 


47.2 
47.8 


55.1 
55.7 


V 




.. 128.0 256.0 


512.0 1000.0 2000.0 


4000.0 


8000.0 


00 


A_ 
A_ 


-33° 
-10° 


.. 65.9 78.8 
.. 66.5 81.7 


93.4 108.6 124.2 
99.2 118.8 140.5 


139.0 
162.5 


153.0 
181.8 


167.5 
199.0 



Again, we find that as the concentration decreases the equivalent con- 
ductance increases and approaches a limiting value in the neighborhood 
of 167.5 at —33°. The ionization of the solutions of potassium iodide 
in sulphur dioxide is, however, markedly lower than that of correspond- 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 49 

ing solutions in acetone and alcohol. At higher concentrations the solu- 
tions of potassium iodide exhibit a marked divergence from the aqueous 
type. While it is true that at —33° the conductance falls throughout 
as the concentration increases, it will be observed that in the concentra- 
tion interval between 7 = 2 and F = 16 the conductance undergoes only 
an inappreciable increase, whereas at both higher and lower concentra- 
tions the conductance change is quite marked. This behavior of the 
more concentrated solutions in sulphur dioxide indicates the appearance 
of a new type of curve. At a slightly higher temperature this irregu- 
larity at the higher concentration becomes more pronounced and a maxi- 
mum and a minimum occurs in the curve, as may be seen from the values 
given for the conductance of these solutions at —10°. The curve at 
— 10° is a typical example which is met with in the case of a large 
number of solvents. 

Before discussing this case in detail, however, let us examine a type 
of solution the conductance curve of which has a form radically different 
from that of aqueous solutions. In Table XIV * are given values of the 
conductance of methyl alcohol in liquid hydrogen bromide at —90°. 

TABLE XIV. 

Conductance of CH3OH in Liquid HBr at — 90°. 

V 0.1250 0.2500 0.500 0.769 1.00 2.00 7.69 

A 0.600 0.631 0.211 0.0378 0.00925 0.001660 0.000615 

It will be observed that in the more dilute solutions the conductance 
diminishes continuously as the concentration decreases. There is no in- 
dication that, at lower concentrations, the conductance approaches a 
limiting value other than zero. In the more concentrated solutions the 
conductance increases greatly as the concentration increases, until a 
maximum is reached, after which the conductance falls off sharply. It 
is interesting to note also that, in this solvent, methyl alcohol functions 
as an electrolyte, although in most solvents methyl alcohol exhibits no 
electrolytic properties. Actually, however, the solutions of methyl alcohol 
in hydrogen chloride do not differ materially in properties from solutions 
of typical salts, such as the substituted ammonium salts in this solvent, 
although the value of the equivalent conductance is larger for typical 

salts. 

Another example of this type of conductance curve is that of solu- 
tions of trimethylammonium chloride in liquid bromine. The values of 
the conductance at 25° are given in Table XV: ^ 

'Archibald, J. Am. Chem. Soc. 23, 665 (1907). 
"Darby, J. Am. Chem. 80c. J,0. 347 (1918). 



50 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE XV. 

Co:jdtjctance op Teimethylammonium Chloride in Bromine at 25°. 

C 0.029 0.0595 0.2093 0.3427 0.5334 0.9323 1.236 1.314 

A 0.0253 0.1038 2.063 6.259 6.469 9.865 11.49 11.00 

This case is, if anything, even more extreme than that of methyl alcohol 
in hydrogen bromide. The increase in the conductance with increasing 
concentration is extremely marked. At a concentration of 0.029 mols 
per liter, the equivalent conductance is only 0.0253, whereas at a concen- 
tration of 1.236 mols per liter the equivalent conductance is 11.49. It is 
to be noted that in the neighborhood of normal the equivalent conduct- 
ance of these solutions in bromine is comparable with that of solutions in 
ordinary solvents. At slightly lower concentrations, however, this is no 
longer the case. For a concentration change in the ratio of 43 to 1, the 
conductance increases in the ratio of approximately 450 to 1. 

It is apparent that the relation between the conductance and the 
concentration, as we observe it in aqueous solutions, is not a property 
characteristic of electrolytic solutions in general. It represents one ex- 
treme of two types of solutions, the other of which is exemplified in 
solutions in hydrogen bromide and in bromine. Between these two ex- 
treme types we have an intermediate type which appears to combine 
the characteristics of these extreme types. A typical example is fur- 
nished by solutions of potassium iodide in methylamine at — 33°, values 
of which are given in Table XVI: ^ 

TABLE XVI. 

Conductance of KI in CH3NH2 at — 33°. 

V .... 0.6094 1.190 2.320 8.833 33.62 107.4 408.9 1557 5927 
A .... 31.12 32.97 28.49 17.40 14.64 17.72 27.79 45.86 74.53 

The conductance curve in this case is intermediate in type between that 
of solutions in water and in bromine. In the more dilute solutions, be- 
ginning at a dilution of approximately 33 liters, the conductance increases 
continuously with decreasing concentration and apparently approaches 
a limiting value. At a dilution of 33.62 liters, the conductance has a 
minimum value. At higher concentrations it increases markedly, reach- 
ing a maximum in the neighborhood of 1.19 liters, after which it again 
decreases. In the more concentrated solutions, therefore, the curve re- 
sembles that of solutions in bromine. 

•Fitzgeiald, J. PTiva. Chem. 16, 621 (1912). 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 51 

These intermediate curves apparently form a continuous series be- 
tween the two extreme types and, by suitably changing the condition of 
the solutions, a continuous shift takes place in the curve from one ex- 
treme toward the other. For example, as the temperature of a solution 
is increased, there is a shift from the aqueous type toward the type 
exemplified by the solutions in hydrogen bromide. This is clearly the 
case with solutions in sulphur dioxide. As we have already seen, at 
— 33° the conductance of solutions in sulphur dioxide increases continu- 
ously with decreasing concentration, although there is a certain concen- 
tration interval over which the conductance change is extremely small. 
At a temperature of — 10° this curve exhibits a maximum and a mini- 
mum, similar to that just described in the case of solutions in methyl- 
amine. At still higher temperatures, the maximum and minimum be- 
come more pronounced. 

Methylamine may be looked upon as a derivative of ammonia and 
the relation between methylamine and ammonia solutions may be ex- 
pected to be similar to that between the alcohols and water. As we 
shall see presently, ammonia solutions, for the most part, belong to the 
aqueous type; that is, the conductance increases throughout with de- 
creasing concentration. In the case of methylamine solutions, as we 
have seen, the curve exhibits a pronounced maximum and minimum. 
Solutions in ethylamine are still further removed toward the bromine 
type, as is apparent from the values given for the conductance of silver 
nitrate in ethylamine in Table XVII: ' 

TABLE XVII. 
Conductance of AgNOg in CjHgNHj at —33°. 



V 


0.9928 


1.981 


3.953 


15.73 


62.65 


125.0 


A 


5.67 


5.820 


4.320 


1.677 


1.038 


1.041 



In this case the conductance decreases with decreasing concentration, but 
it is evident that at the lower concentrations the conductance does not 
approach the value zero as a limit. In fact, it is apparent that, at dilu- 
tions slightly greater than 125 liters per mol, the conductance curve will 
again rise. Indeed, solutions of certain other salts in ethylamine exhibit 
a distinct minimum in the neighborhood of 0.01 normal. The conductance 
curve of solutions in amylamine resembles that of solutions in bromine 
very closely, the conductance decreasing throughout with decreasing con- 
centration and apparently approaching a value of zero so far as has 
been observed. 

' Fitzgerald, loo. cit. 



52 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

It is evident that, in order to account for the phenomena of electro- 
lytic solutions, it is necessary to take into consideration the fact that 
the form of the conductance curve as observed in water is not a general 
type, but is only one extreme of several types. Any coinprehensive 
theory of electrolytic solutions must obviously account for both types. 

The only non-aqueous solvent with regard to whose solutions we have 
anything like complete information at the present time is liquid ammonia. 
This solvent yields electrolytic solutions with an extremely large variety 
of substances and we shall have frequent occasion to refer to these 
solutions below. At this point it will be sufficient to give an example of 
the conductance curve for a typical salt dissolved in liquid ammonia. 
In Table XVIII " are given values of the conductance of solutions of 
potassium nitrate in liquid ammonia at its boiling point, approximately 
—33°, at a series of dilutions. It is evident that these solutions belong 
to the aqueous type, the conductance increasing throughout with decreas- 
ing concentration and approaching a limiting value at very low concen- 
trations. The limiting value for potassium nitrate is 339." 

TABLE XVIII. 
Conductance of KNO, in NH, at — 33°. 



V .... 


324 


1001 


2514 


6162 


23060 


69820 


00 


A ... 


. . . 192.7 


245.0 


282.7 


309.9 


330.1 


338.6 


339. 


Y .... 


... 0.567 


0.720 


0.831 


0.912 


0.972 


0.995 





Solutions of typical salts in liquid ammonia exhibit a somewhat higher 
conductance than do the corresponding salts in water, but it is evident 
that the ionization of these salts in liquid ammonia solutions is consid- 
erably lower than in water, as may be seen from Figure 3. Ammonia 
apparently approaches ordinary alcohol and acetone in its ionizing power. 
In the case of certain solutions in liquid ammonia, an intermediate type 
of conductance curve is found. This is the case, for example, with potas- 
sium amide whose curve exhibits a minimum.^" 

A similar, but in some respects a slightly different, case is found in 
certain of the cyanides, of which mercuric cyanide and silver cyanide 
may serve as examples. The conductance values for solutions of mer- 
curic cyanide in ammonia are given in Table XIX.^^ 

'Franklin and Kraus, Am. Chem. J. 23, 277 (1900). 
•Kraus and Bray, J. Am. Chem. Soc. S5, 1337 (1913). 
"Franklin, Ztschr. f. phps. Chem. 69, 290 (1909). 
" Franklin and Kraus, loc. cit. 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 53 

TABLE XIX. 

Conductance of Hg(CN)2 in NH3 at —33°. 

X ••• 116 3.37 5.71 21.8 33.0 55.6 

^ 2.48 1.86 1.79 1.63 1.64 1.75 

The solutions of this salt exhibit a conductance curve with a very flat 
minimum, the curve thus being similar to that of potassium iodide in 
methylamine. Silver cyanide likewise exhibits a curve with a minimum. 
The values are given in Table XX.^^ 

TABLE XX. 

Conductance of AgCN in NH3 at — 33°. 

F .... 4.48 9.02 17.85 35.25 69.69 137.7 272.8 538.0 1063.0 
A .... 15.58 15.39 14.28 13.45 12.83 12.41 12.12 12.00 12.00 

It is evident from these values that the conductance curve for silver 
cyanide has a very flat minimum in the neighborhood of 10"^ normal. 
What is more striking, however, is the fact that the conductance changes 
so little with the concentration. The entire change between 10"^ normal 
and 0.5 normal is only from 12.00 to 15.5 or about 30 per cent. 

We see that solutions in non-aqueous solvents exhibit a great variety 
of properties many of which diverge largely from those of aqueous solu- 
tions. A great variety of liquids are capable of forming electrolytic solu- 
tions with various substances and many substances which do not form 
electrolytic solutions when dissolved in water form such solutions in 
other solvents. 

2. Applicability of the Mass-Action Law to Non-Aqueous Solutions. 
From a study of aqueous solutions of electrolytes, the conclusion was 
reached that the conductance is due to the motion of charged carriers 
through these solutions and that these charged carriers are in equilibrium 
with the neutral molecules of the electrolyte. In other words, the elec- 
trolyte is dissociated, or ionized, to use the accepted term for this process, 
and the degree of ionization may be measured by means of the ratio of 
-the equivalent conductance of the solution to the limiting value which the 
equivalent conductance approaches as the concentration diminishes in- 
definitely. If this hypothesis is correct, then, as we have seen, the mass- 
action law should apply, and, if the laws of dilute solutions may be 
assumed to hold. Equation 7 expresses the relation between the con- 
ductance and the concentration of an electrolytic solution. It was found 

" Franklin and Kraus, loo. cit. 



54 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

that this relation is fulfilled in the case of aqueous solutions of weak acids 
and bases, but is not fulfilled in the case of solutions of electrolytes which 
are more largely ionized. 

It is at once apparent that non-aqueous solutions furnish exceptions 
to the simple mass-action law, since we have here cases in which the 
conductance increases with increasing concentration, which result is not 
in accord with Equation 7. To solve the problem resulting from this 
discrepancy, three methods of attack at once present themselves. In the 
first place, the ionization may not be correctly measured by the ratio 
A/Ao. Then, again, we may assume that the reaction equation on which 
the calculations are based is not correct. Finally, we may assume that 
the equilibrium is of the type as assumed, but the conditions assumed 
in deriving the mass-action law are not fulfilled in the solutions in ques- 
tion; in other words, the solutions may not be considered as dilute. It 
is of course impossible to state on a priori grounds the concentration at 
which the deviations from the laws of dilute solutions will become appre- 
ciable. The only method that we have of attacking this problem at 
present is to carry out measurements at different concentrations and 
examine the change in the mass-action function as the concentration de- 
creases. If the fundamental assumption underlying the hypothesis of 
Arrhenius is correct, then the mass-action function should approach a 
definite limiting value as the concentration decreases. 

Let us examine, therefore, the conductance curves of the more dilute 
non-aqueous solutions in order to determine whether the mass-action 
fmiction approaches a definite limiting value. It is obvious that, in order 
to calculate the degree of ionization, the value of Ao must be known and 
this value can be obtained only by extrapolation. If the mass-action 
equation in its simple form actually holds, then it is possible to determine 
the value of Ao by a very simple graphical extrapolation. Equation 7 
may be written in the form: 

(8) CA = :!^ KAo. 

It is obvious that, if this equation holds, the reciprocal of the equivalent 
conductance. A, is a linear function of CA, which is equal to the specific 
conductance multiplied by 10'. In other words, if the mass-action law 
is obeyed, the reciprocal of the equivalent conductance and the specific 
conductance are connected by means of a linear equation. If, therefore, 
the experimental values of CA and of 1/A are plotted in a system of rec- 
tangular co-ordinates, the points will lie on a straight line if the mass- 
action law holds. This straight line extrapolated to the axis of 1/A 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 55 

yields the value of Ao while, obviously, the value of K results from the 
slope of the curve. 

Leaving aside for the moment the exact values of Ao, we may roughly 
compare the variation of the function K for solutions in different solvents. 
In Table XXI" are given the values of this function for potassium 
nitrate dissolved in ammonia and in water at corresponding degrees of 
ionization. 

TABLE XXI. 
Valxies of K for Solutions of KNO3 in NH3 and H2O. 



Y 


if NH3 X 10- 


%20 


57.00 


0.2277 


1.279 


70.00 


0.197 


0.9528 


85.59 


0.167 


0.3389 


91.66 


0.1635 


0.2332 


94.30 


0.1699 


0.1710 



It is at once apparent that the variation of the function K in dilute am- 
monia solutions is much less than it is in aqueous solutions. Indeed, 
between the ionization values of 70% and 94% the value of the con- 
ductance function for potassium nitrate in ammonia changes only by a 
few per cent, whereas, in aqueous solutions, this function increases ap- 
proximately five times. Apparently, therefore, dilute solutions in am- 
monia approach the mass-action law much more nearly than do solutions 
of the same substances in water. 

A circumstance which greatly facilitates the study of the applicability 
of the mass-action law to dilute solutions in non-aqueous solvents is the 
relatively low ionization of the solutions in these solvents. In the case 
of the strong electrolytes in water, a comparison of the experimental re- 
sults with the mass-action law is rendered difficult by the high ionization 
of these salts. Since the expression 1— Yj the value of the un-ionized 
fraction, appears in the denominator of the mass-action expression, and 
since y is very nearly unity, it follows that the equivalent conductance 
must be determined with a high degree of precision in order to determine 
the applicability of the mass-action function. It is only in the case of 
potassium chloride that sufficiently precise data are at hand to make a 
study of this kind possible in aqueous solutions, and even in this case the 
results of such a comparison remain uncertain. 

Only a small portion of the data relating to the conductance of non- 
aqueous solutions has sufficient precision to make a comparison with the 
consequences of the mass-action law possible. It is only in the case of 

"Franklin and Kraus, Am. Chem. J. US, 299 (1900). 



56 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

solutions in liquid ammonia that we have such data relating to a large 
number of electrolytes. Kraus and Bray " have examined the conduct- 
ance of ammonia solutions from this point of view. In Figures 4 and 5 
are plotted values of the reciprocal of the equivalent conductance as 




7-5 IO.O 

looo(cA) 



I2.J 



15.0 



17.5 



Fig. 4. Showing Approach of Dilute Solutions in Liquid NHs to the 
Mass-Action Law. 



ordinates against values of the specific conductance as abscissas. In 
Figure 4 the symbol of the electrolyte is shown in the figure, while in 
Figme 5 the curves in order from 1 to 7 are for: 1, thiobenzamide; 2, 
orthomethoxybenzenesulphonamide; 3, paramethoxybenzenesulphona- 



" Kraus and Bray, J. Am. Ohem. Boo. SS, 1315 (1913). 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 



57 



mide; 4, metamethoxybenzenesulphonamide; 5, nitromethane; 6, sodium- 
nitromethane; and 7, orthonitrophenol. Examining tiie figure for the 
typical salts, it will be observed that in the case of silver iodide, am- 
monium chloride, potassium nitrate, and ammonium nitrate the curves 




loo(cA) 

Fig. 5. Showing Approach of Dilute Solutions of Organic Electrolytes in NS, to 

the Mass-Action Law. 

in dilute solution approach a straight line. In the case of ammonium 
bromide and potassium iodide the number of points is not sufficient to 
actually determine the form of the curve in dilute solutions. In the case 
of other salts, the figures of which are not shown here, similar results 
were obtained; that is, in those cases where sufiicient data are available 
at low concentrations, the points approximate a straight line and this 



58 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

is the more true the more consistent the data are among themselves. In 
the case of the seven electrolytes in Figure 5, the correspondence with 
the mass-action law is much more certain. One reason for the better 
agreement in the case of these electrolytes is their lower ionization, as 
a result of which errors in the value of the equivalent conductance pro- 
duce a smaller variation in the mass-action constant. Moreover, in these 
cases the mass-action law appears to apply to greater total salt concen- 
trations. In view of the fact that the original experimental results are 
independent of any considerations as to the applicability of the mass- 
action law, the conclusion appears justified that in the case of solutions 
in liquid ammonia the mass-action function approaches a limiting value 
at low concentrations. 

The total salt concentration at which the deviations from the simple 
mass-action law become appreciable is the lower, the greater the ioniza- 
tion of the electrolyte. In this respect solutions in ammonia resemble 
solutions of the acids and bases in water. The lower the ionization of 
an acid or a base in water, the higher the concentration up to which the 
mass-action law appears to hold. From an examination of their results, 
Kraus and Bray drew the conclusion, however, that the deviations from 
the mass-action law become appreciable for different electrolytes in 
ammonia solution at about the same ion concentration. They found 
that the mass-action function for a number of electrolytes was increased 
over the limiting value by 5% at ion concentrations lying in the neigh- 
borhood of 1 X 10'* N. It is, however, apparent that in certain cases the 
ion concentration is considerably greater and in other cases considerably 
lower than this value. So, for example, in the case of potassium amide 
this concentration is 2.76 X 10'*, while in that of trinitraniline it is 
0.22 X 10'*. 

We may now consider the values of the mass-action constant for 
different electrolytes in ammonia solution. The values for the inorganic 
electrolytes are given in Table XXII ^° (see opposite page) . 

It is apparent, in the first place, that the values of the mass-action con- 
stant for the different inorganic electrolytes differ considerably. The ex- 
treme values lie between 0.056 X 10'* for sodium amjde and 42 X 10'* 
for potassium iodide. The greater number of the salts, however, have 
ionization constants lying between 21 X 10'* and 28 X 10'*. This varia- 
tion of the ionization constants for different inorganic electrolytes in am- 
monia is in striking contrast with the nearly identical ionization of the 
same electrolytes in water. It should be borne in mind, however, that in 
aqueous solution the degree of ionization is so high, in any case, that dif- 

" Kraus and Bray, loe. cit. 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 59 

TABLE XXII. 
Values of K and Ao for Different Electrolytes in NH3 at 33°. 

Salt WK Ao 

NaNH^ 0.056 263 

KNH, 1.20 301 

Agl 2.90 287 

NH.Cl 12.0 310 

NaCl 14.5 309 

KNO3 15.5 339 

KBr 21.0 340 

TINO3 21.0 323 

NaBrOg 23.0 378 

NaNOg 23.0 301 

NH^Br 23.0 303 

LiNOa 26.0 283 

NaBr 27.0 302 

Nal 28.0 301 

AgNOg 28.0 287 

NH^NOg 28.0 302 

KI 42.0 339 

ferences in the ionization values of the different electrolytes are neces- 
sarily very small. Nevertheless, we must conclude that the ionization 
values of typical salts in water are much more nearly the same in that 
solvent than they are in ammonia or in any other solvent for which 
reliable data are available. The order of the ionization constants does not 
appear to bear any relation to the constitution of the electrolytes. So 
ammonium chloride has an ionization constant of 12 X 10"* and am- 
monium nitrate of 28 X 10'*, while silver iodide has an ionization con- 
stant of 2.9 X 10"* and silver nitrate 28 X 10~*. Sodium nitrate has a 
greater ionization constant than potassium nitrate, while sodium iodide 
has a smaller ionization constant than potassium iodide. 

The constants for sodium and potassium amides are of interest owing 
to the fact that these substances are bases in liquid ammonia solution. 
Apparently these substances are relatively weak bases when compared 
with the typical salts in ammonia or when compared with corresponding 
bases in water. Indeed, it is apparent that all electrolytes in ammonia 
solution have comparatively small ionization constants. For example, 
the ionization constant of acetic acid in water is 0.182 X 10"*. The 
ionization constant of this acid, therefore, is approximately three times 
that of sodium amide and 1/7 that of potassium amide. 

The ionization constants for a number of organic electrolytes in liquid 



60 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ammonia are given in Table XXIII.^" Here, again, we find a large varia- 
tion in the value of the ionization constant for different electrolytes. 

TABLE XXIII. 
Values of K and of Ao for Organic Electrolytes in NH3 at — 33°. 

Salt 10* K Ao 

Cyanacetamide 0.045 260 

Thiobenzamide 0.40 204 

Orthomethoxybenzenesulphonamide 0.40 208 

Paramethoxybenzenesulphonamide 0.50 208 

Nitromethane 0.53 278 

Sodiumnitromethane 0.78 278 

Benzenesulphonamide 1.39 208 

Metamethoxybenzenesulphonamide 1.81 208 

Orthonitrophenol 3.90 246 

Methylnitramine 8.4 256 

Phthalimide 8.7 248 

Benzoicsulphinide 12.0 206 

Metanitrobenzenesulphonamide 12.5 231 

Potassiummetanitrobenzenesulphonate 15.0 275 

Nitrourethaneammonium 21.6 262 

Trinitrobenzene 30.0 234 

Trinitraniiine 30.0 234 

The strongest of these, trinitraniiine and trinitrobenzene, have ionization 
constants as great, or greater, than those of typical salts in ammonia. 
On the other hand, cyanacetamide has an ionization constant of only 
0.045 X 10"*. Cyanacetamide, therefore, is a weaker acid in ammonia 
solution than acetic acid is in water, and of course a much weaker acid 
than cyanacetic acid in water. In other respects, as regards the relation 
of the ionization constants of these electrolytes to their constitution, we 
find relations similar to those in aqueous solutions. The introduction of 
strongly electronegative groups into the negative constituent increases 
the value of the ionization constant. It will be observed that many of 
the organic substances which act as electrolytes in ammonia solution are 
not electrolytes in water. This is true of nearly all the acid amides and 
of such compounds as trinitrobenzene. The positive ion, in the case of 
the acid amides, as indeed in the case of all the acids in ammonia solu- 
tion, is presumably the ammonium ion.^' 

Having seen that the mass-action law applies to dilute solutions of 
' practically all electrolytes in ammonia, we may inquire whether the same 

" Eraus and Bray, loc. cit. 
" IbU., loc. cit., p. 1357. 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 



61 



is true of solutions in other non-aqueous solvents. In Table XXIV ■^* 
are given values of the mass-action constants for sodium iodide in a num- 
ber of different solvents. In Figure 6 are plotted values of the reciprocal 
conductance against those of the specific conductance for these solutions. 




234567 

ioo(<;A} [for Isoamylalcohol iooo(cA)] 

Fia. 6. Showing how Solutions of Binary Electrolytes in Different Solvents Approach 
the Mass-Action Relation at Low Concentrations. 

An examination of the figure shows that in all cases the conductance 
curves approach a linear relation in the more dilute solutions. We may 
conclude, therefore, that in the case of non-aqueous solvents, in general, 
the mass-action law is approached as a limiting form at low concentra- 
tions. 

M Kraus and Bray, loo. cit. 



62 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE XXIV. 
Values of K and of Ao foe Electrolytes in Different Solvents. 

Solvent Solute Temp. °C. iC X 10* A„ 

Benzonitrile Nal 25° 55.0 49.0 

Epichlorhydrin (CA),NI 25° 48.5 62.1 

Propylalcohol Nal 18° 45.0 20.6 

Acetone Nal 18° 30.0 167.0 

Acetophenone Nal 25° 34.0 35.6 

Methylethylketone Nal 25° 23.0 139.0 

Pyridine Nal 18° 13.0 61.0 

Isobutylalcohol Nal 25° 12.0 13.7 

Acetoaceticester NaSCN 18° 9.5 ' 32.1 

Isoamylalcohol Nal 25° 3.9 9.2 

Ethylenechloride (C3H,),NI 25° 1.45 66.7 

The mass-action constant varies with the nature of the solvent. The 
greatest value is that for benzonitrile, which is 55 X 10"*, and the smallest 
that for ethylenechloride, which is 1.45 X 10"*. The change in the value 
of the ionization constant among the alcohols is of particular interest in 
view of their relation to water. The constant for solutions in propyl 
alcohol is 45 X 10'*, in isobutylalcohol 12 X 10"*, and in isoamylalcohol 
3.9 X 10"*. It is evident that, as the substituting hydrocarbon group 
becomes more complex, the ionization constant decreases. These results 
also have a bearing on the probable behavior of aqueous solutions. The 
properties of solutions in the lower alcohols differ only inconsiderably 
from those of aqueous solutions. It seems probable, therefore, that in 
going from water through the lower alcohols to the higher alcohols the 
change in the phenomenon underlying the ionization process undergoes 
an alteration in degree rather than in kind. It might be concluded, 
therefore, that in aqueous solutions, also, the mass-action law is ap- 
proached as a limiting form. This question, however, will be discussed 
at somewhat greater length in a succeeding chapter. 

A considerable number of data are available on the conductance of 
dilute solutions in acetone. In the following table are given values of 
the mass-action constant and the limiting values of the equivalent con- 
ductance for a series of electrolytes in this solvent. 

TABLE XXV. 

Values of K and of Ao for Different Electrolytes in Acetone at 18°. 

Solute 10* K Ao 

KI 51.0 156 

Nal 39.0 156 

Lil 31.0 154 - "' 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 63 

TABLE XXY.— Continued. 
Solute 10* K A„ 

NHJ .• 15.0 159 

KSCN 31.0 169 

LiSCN 18.0 167 

NH.SCN 8.3 172 

KBr 16.0 156 

NaBr 13.0 156 

LiBr 5.7 154 

NH^Br 2.3 159 

LiNOs 2.6 125 

AgNOg 0.28 100 

LiCl 0.94 154 

From an examination of this table it is obvious that the ionization con- 
stants of typical salts in acetone vary within very wide limits. So, the 
ionization constant for silver nitrate is 0.28 X 10"*, whereas that for 
potassium iodide is 51.0 X 10"*. More remarkable still is the regularity 
in the variation of the constants as a function of the constitution of the 
electrolyte. The ionization constants of the iodides diminish in the order 
potassium, sodium, lithium, ammonium. The same order holds in the 
case of all other salts, namely the sulfocyanates, bromides, and nitrates. 
On the other hand, the ionization constants of salts with a common posi- 
tive ion vary in the order: iodides, sulfocyanates, bromides, nitrates, 
chlorides. This order holds true in every case. It appears, therefore, 
that the ionization constant K is an additive function of the constituent 
ions of the electrolytes. This is the only solvent for which such a rela- 
tion appears to hold true. What the significance of this may be is at 
present uncertain. It is important, however, to observe that the ioniza- 
tion of different typical salts in acetone varies within extremely wide 
limits. The similarity in the behavior of strong electrolytes in aqueous 
solutions, as regards their ionization, is therefore not to be considered as 
a property which may be ascribed primarily to the electrolytes them- 
selves, but rather one in which the solvent itself appears as the chief 
factor. 

3. Comparison of the Ion Conductances in Different Solvents. If 
the values of Ao are known and if the transference numbers of the 
electrolytes are known, then the values of the ion conductances may be 
determined. However, before proceeding to a comparison of the values 
of the ion conductances in different solvents, it will be well to point out 
that the value of Ao is dependent upon the form of the extrapolation 
function which must be assumed. Only in the case of solutions which 



64 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

approach the mass-action law as a limiting form may we be reasonably- 
certain that the extrapolated value of A„ is correct. In other cases, 
therefore, the limiting conductance values are more or less arbitrary. In 
a subsequent chapter this question will be discussed somewhat more at 
length. For the present we shall assume that the Ao values obtained by 
the ordinary methods of extrapolation are approximately correct. 

The values of the equivalent conductances of the different electrolytes 
in ammonia and water have been given in Tables III, XXII and XXIII. 
In comparing the conductances in the two solvents, however, it is pre- 
ferable to compare the conductance of the individual ions, rather than 
that of the sum of the ions of any given electrolyte. Before proceeding 
further, therefore, we shall resolve these values of the conductance for 
the various electrolytes into two parts, namely the conductance of the 
positive and of the negative ion respectively. In order that this may be 
done, it is necessary that the transference number of at least one elec- 
trolyte shall be known. In the case of ammonia solutions the transfer- 
ence nimibers of a considerable number of electrolytes have been deter- 
mined by Franklin and Cady.^^ With the aid of their data, the follow- 
ing values of the equivalent conductance of the typical inorganic ions 
have been calculated.^" For the sake of comparison, the ion conduct- 
ances of the same ions in water at 18° are given as well as the ratio of 
the ion conductances in ammonia and in water. 

TABLE XXVI. 

Ion Conductances in Ammonia and in Water. 

Ion InNHj InH.O A.nh/-^H,0 

Positive Li* 112 33.3 3.36 

Ag* 116 54.0 2.15 

Na* 130 43.4 3.00 

NH,* 131 64.7 2.03 

Th 152 65.9 2.31 

K* 168 64.5 2.61 

Negative BrOg- 148 47.6 3 11 

NO3- 171 61.8 2.77 

I- 171 66.6 2.57 

Br- 172 67.7 2.54 

CI- 179 65.5 2.73 

NH^- 133 

"Franklin and Cady, J. Am. Chem. Soc. 26, 499 (1904). 
»" Kraus and Bray, loo. cit. 



ELECTROLYTIC SOLUTIONS IN VARIOUS SOLVENTS 65 

It will be observed that the ion conductances in ammonia and in 
crater do not stand in a fixed ratio. For example, for the silver ion, the 
ion conductance in ammonia is 2.15 times that in water, whereas for 
the lithium ion the conductance in ammonia is 3.36 times that in water. 
Similarly, the conductance of the bromide ion in ammonia is 2.54 times 
that in water, while the conductance of the bromate ion is 3.11 times 
that in water. We may naturally inquire as to what are the factors 
upon which depends the conductance of different ions in different solvents. 

If the current is carried through a solution by the translation of 
charged particles of molecular dimensions, then we should expect the 
speed of these particles to be a function of the viscosity of the medium 
through which they move. It might be assumed, for example, that the 
conductance is proportional to the reciprocal of the viscosity, or to the 
fluidity of the solvent. The viscosity of water at 18° is 10.63 X 10"^ and 
that of ammonia is 2.558 X lO"" at its boiling point. Consequently the 
fluidity of ammonia is 4.15 times as great as that of water. If the con- 
ductance of the ions were directly proportional to the fluidity of the 
solvent, then the conductance of all ions in ammonia should be 4.15 times 
as great as that of the same ions in water. We see, however, that while 
the conductance of the various ions in ammonia is markedly greater 
than that in water, nevertheless the ratio of the ion conductances in the 
two solvents is in all cases smaller than this value. Furthermore, the 
effect is one specific with respect to the individual ions. For example, 
for the sodium ion, the value is 3.0, while for the lithium ion it is 3.36. 
It is noticeable that the ratio for the ions increases in the order: am- 
monium, potassium, sodium, lithium. In other words, in ammonia the 
lithium ion possesses a relatively much higher conductance with respect 
to water than does the ammonium ion. 

The same general relations hold in the case of the negative ions. The 
conductance of the bromate ion in ammonia is 3.11 times that in water, 
whereas that of the bromide ion is only 2.54 times that in water. On 
the whole, the ion conductances in ammonia vary less than they do in 
water. The extreme variation in the case of ammonia solutions is fronj 
112, for the lithium ion, to 168, for the potassium ion, or a ratio of 1.5, 
whereas in the case of aqueous solutions the extreme variation is from 
33.3, for the lithium ion, to 65.9, for the thallous ion, or a ratio of 1.98. 
For the negative ions in ammonia solution the extreme ratio is 1.21, 
whereas for aqueous solutions it is 1.37. In general, however, the order 
of ionic conductances in the two solvents is the same. With a few ex- 
ceptions, ions which move very slowly in water also move very slowly 
in ammonia. 



66 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

It is evident that the conductance of an ion is a function of the con- 
stitution of the solvent as well as of that of the ion itself. In this con- 
nection it should be observed that a given electrolyte dissolved in two 
different solvents does not necessarily yield the same ions. In other 
words, complexes may be formed between the ions and the solvent proper- 
ties of which will depend upon the nature of the solvent. It is well 
known that certain ions tend to form complexes with certain solvents. For 
example, the silver ion forms a complex with ammonia even in aqueous 
solutions. It may be assumed, therefore, that the silver ion has a great 
tendency to form complexes with ammonia. The cause for the relatively 
low value of the conductance of the silver ion in ammonia may be 
ascribed to the formation of a relatively large complex silver-ammonia 
ion in ammonia solution. Similarly, those ions whose salts show a 
marked tendency to form complexes with water, which, for example, 
give stable crystalline hydrates, show a relatively higher speed in am- 
monia than in water. Thus, the speed of the lithium ion in ammonia is 
relatively much greater with respect to its speed in water than is that 
of the potassium ion. We may therefore conclude that the lithiiun ion 
is relatively less complex in ammonia than it is in water. 



Chapter IV, 
Form of the Conductance Function. 

1. The Functional Relation between Conductance and Concentra- 
tion. If an equilibrium exists between the ions and the un-ionized mole- 
cules in a solution, then the relation between the conductance and the 
concentration is expressed by Equation 7, which follows from the mass- 
action law. We have seen that this equation is fulfilled in solutions of 
weak electrolytes in water and that it is approached as a limiting form 
in solutions of strong electrolytes in non-aqueous solvents. This equa- 
tion is the only one so far suggested to account for the relation between 
the conductance and the concentration which has a substantial theoretical 
foundation for its support. At higher concentrations, in the case of the 
stronger electrolytes, both in water and in non-aqueous solvents, the 
simple form of the mass-action law no longer holds. Except at very 
high concentrations, where viscosity effects become pronounced, the con- 
ductance in all cases varies in such a way that the value of the mass- 
action function increases with increasing concentration. If the reciprocal 
of the equivalent conductance is plotted against the specific conductance, 
then, in the case of strong electrolytes, it is found that the experimental 
curve is concave toward the axis of specific conductances. 

We have seen that in different solvents the conductance curve, as a 
function of the concentration, varies greatly in form, and the conclusion 
might be drawn that the process involved in these solutions is entirely 
different in character. Since the form of the conductance function in 
the case of the concentrated solutions is thus far not determinable from 
theoretical considerations, various attempts have been made to deter- 
mine empirical functions which should express the conductance in terms 
of the concentration. In the case of aqueous solutions the equation of 
Storch 1 appears to apply over a considerable concentration range. This 
equation may be written in the form: 

(9) K' = ^^^ = D{Cyr, 

where D and m are constants. This equation applies remarkably well 
in the case of aqueous solutions, even up to high concentrations. It will 

•Storcli, Ztschr. f. phys. Ohem. 19, 13 (1896). 

67 



68 



PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



be observed that in this equation the mass-action function K' is expressed 
as a function of the ion concentration raised to the m'th power. The 
equation may be tested very simply by graphical methods. It may be 
written in the form: 
(10) (2 — m) log (Cy) — log [C (1 — y) ] = log D. 

If, therefore, we plot the logarithms of C{l—y) against the logarithms 
of the ion concentrations Cy or the specific conductances, the experi- 
mental points should lie on a straight line, provided the equation holds. 
This method of treatment was first proposed by Bancroft ^ and has 
proved extremely useful in determining the behavior of very concen- 
trated solutions. In Figure 7 are shown the curves for potassium chloride 
and potassium nitrate in water at 18°. It will be observed that the points 
lie very nearly on a straight line. 



o 







/ 



3.0 



O 



o 

bu 
O 



4.0 

+0 So Z.0 /~o *•" 

LogC (1-Y). 
Fig. 7. Plot of Storch Equation for Aqueous Solutions of Binary Electrolytes. 

It is evident, however, that an equation of this type cannot apply 
generally, since it does not approach the mass-action expression as a 
limiting form. As we have seen, dilute solutions in non-aqueous solvents 
approach the mass-action function at low concentrations. It has there- 
fore been proposed ' to express the relation between the conductance and 
the concentration by means of the equation: 



(11) 



K 



C(l-Y)~ 



D(Cy)"' + K 



2 Bancroft, Ztschr. f. phya. Ohem. SI, 188 (1899). 

" Kraus, Proc. Am. Chem. Soc. 1909, p. 15 ; Bray, Science S5, 433 (1912) ; Trans. Am. 
Electro-Ch. Soc. 21, 143 (1912) ; MacDougall, J. Am. Ohem. Soc. Si, 855 (1912) ; Kraua 
and Bray, J. Am. Ohem, Soc 3S, 1315 (1913). Soniewliat similar tour-constant equations 



FORM OF THE CONDUCTANCE FUNCTION 69 

In this equation y is written for the ratio -r- for the sake of brevity. An 

° 
inspection of this equation shows that at low concentrations the first 

term of the right-hand member, involving the ion concentration Cy, will 
diminish as the concentration decreases, and will ultimately become neg- 
ligible in comparison with the constant K. On the other hand, at higher 
concentrations, the constant K will become negligible in comparison with 
the term involving the ion concentration. In other words, at high con- 
centrations this equation approaches the Storch Equation 9 as a limiting 
form. 

Obviously, this equation involves the four constants A^, K, D and m. 
These constants may in most cases be determined readily by graphical 
means. If conductance data are available at very low concentrations, 
the second term of the right-hand member may be neglected, in which 
case the reciprocal of the equivalent conductance becomes a linear func- 
tion of the ion concentration; that is, the equation degenerates into the 
form of Equation 7. The value of Ao and of K may therefore be de- 
termined with a considerable degree of precision from this plot. Hav- 
ing determined these two constants, the values of m and D may be de- 
termined from data at higher concentrations. At very high concentra- 
tions K may be neglected and from a plot of Equation 10, which is 
linear if the equation holds, the values of m and D may be determined. 
In case the constant K is not negligible at higher concentrations, it is 
necessary to take this into account. This may be done by means of a 
second approximation. It is seen from Equation 11 that the mass-action 

function K' = :; — '— is a linear function of the ion concentration raised 
1 — Y 

to the m'th power. If the value of m in the more concentrated solutions, 
as determined by the first approximation, is correct, then the values of 
K aild D may be corrected by means of a plot of K' against (Cy)"*. 
The value of K is then determined by extrapolating to the concentration 
zero and the value of D is determined frqm the slope of the line. The 
values of the Constants having bfeen determined, it is possible to calcu- 
late the conductance of a given electrolyte at any desired concentration 
and to compare the calculated with the experimental values. 

In Figure 8 is shown a plot of the reciprocal of the equivalent con- 
ductance against the specific conductance or ion concentration for solu- 
tions of potassium amide in liquid ammonia.* This plot yields for Ao 

have been proposed by Bates (J. Am. Ohem. Soc. 37, 1431 (1915)) and by de Szyszkowski 
(Uedd K Yet. Akad's Nohelinstitut, Vol. 3, Nos. 2 and 11 (1914)). While these latter 
eauations represent the course of the conductance curve fairly well in the case of aqueous 
Bolutions they are not generally applicable to non-aqueous solutions. 
'Franklin, Ztschr. f. phys. Chem. 69, 290 (1909). 



70 ^PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the value 301 and for K the value 1.26 X lO"*." That is, the straight 
line drawn corresponding to this slope passes through the points in the 
more dilute solutions. 



-l< 



30 












^ 


^ 


^ 


IS 








^ 


^ 








10 




1 


^ 












s 


Aa.30119 


- 















Fig. 8. A„ 



7.5 10 H.5 15 

100 (CA). 
-K Plot for KNa in NHa. 



Having determined the preliminary values of K and of Ao, we may- 
plot the values of the logarithm of K'—K against the logarithm of Cy. 
The plot for this function is shown in Figure 9, where it will be observed 



1.0 



2.0 



.j|f3.< 



^.o 



5.0 











m-i.n ^^-^ 


■% 






-^ 


/ 


D-a093 






^ 


^ 








^ 













3.0 



3.5 



1.0 



2.0 2.5 

lK>g (C7) 

Fig. 9. M — D Plot for KNHj in NHa. 



I.S 



0.0 



that the points lie upon a straight line well within the limits of experi- 
mental error. This plot yields a value of D = 0.095 and m =: 1.18. 
Finally, in order to obtain a more precise value of K, values of K^ are 

■Eraus and Bray, loo. cit. 



FORM OF THE CONDUCTANCE FUNCTION 



71 



plotted against the values of the ion concentration to the power 1.18. 
This plot is shown in Figure 10. The value for D in this case is not 
altered from that originally determined, but the value of K is altered 
from 1.26 to 1.20. 

It will be observed that, throughout, the points lie upon a straight 
line within the limits of experimental error. The equation connecting 



^ o 

















^ 















^ 












0.0099 ^ 


^ 











^^■'^ 


-0^ 










) 


J,'' . 















a.S 5.0 75 "oo "S '5 

io*(<;7)"' 

Fia. 10. K—B Plot for KNa in NHs. 



I7.S 



the equivalent conductance with the concentration for solutions of potas- 
sium amide in liquid ammonia is, therefore: 

^r = -j^l>^ = 0.095 (Cy) ^-^ + 1.20 X 10-* 
C(l — y) 



where Y=3oj. 

The calculated values are compared with the experimental values m 
Figure 11, where the equivalent conductances are plotted as ordinates 
against the logarithms of the concentrations as abscissas. It will be ob- 
served that the calculated curve corresponds with the experimental curve 
up to a concentration of approximately 2 normal. Beyond this concen- 
tration the experimental curve departs rapidly from the calculated curve. 
As we shall see presently, at higher concentrations, the viscosity of the 
solutions increases very largely and it is therefore not possible to test 
the applicability of the equation at these concentrations. 

It becomes a matter of interest to determine whether an equation of 



172 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



this type is generally applicable to solutions of electrolytes in various 
solvents. Since a larger amount of experimental material is available 
for solutions in liquid ammonia than for solutions in any other solvent, 
we may consider solutions in this solvent first. Since the more dilute 
solutions have already been considered and found to conform to the 



aSo 


N 
















AACi 


















<200 
•St/!/.. 






















\ 












Equivalent Con 






\ 
















o\ 


, 
















%SP 


















^^ 


^^:rr 


»««m<a^ 


-^ 



5.0 



40 



t.o 



0.0 



I.O 



3-0 2.0 

Log C. 
FiQ. 11. Comparison of Experimental Values with Equation 11 for KNIL in NHa. 

mp,ss-action law as a limiting form, it follows that the equation will be 
applicable to the more dilute solutions in any case. It remains, there- 
fore, to determine whether the equation likewise applies to the more 
concentrated solutions. 

Kraus and Bray,« who have examined the applicability of this equa- 
tion to a large number of non-aqueous solutions, including solutions in 
ammonia, have concluded that the experimental values may be repre- 

• Kraus and Bray,. loc. c(t. 



FORM OF THE CONDUCTANCE FUNCTION 



73 

sented by an equation of this type within the limits of experimental 
error. In general, it has been found that the more consistent the ex- 
perimental data are among themselves, the more nearly do they adjust 
themselves to Equation 11. The results for inorganic electrolytes dis- 
solved in ammonia are summarized in Table XXVII. 

TABLE XXVII. 

Constants op the Conductance Function for Inorganic 
Electrolytes in NH3 at — 33°. 

Electrolyte WK m D 

KNH^ 1.20 1.18 0.095 

Agl 2.90 0.70 0.009 

NH,C1 12.0 0.84 0.127 

KNO3 15.5 0.96 0.25 

NaNOs 23.0 0.89 0.32 

NH^Br 23.0 0.82 0.24 

LiNOg 26.0 0.86 0.34 

Nal 28.0 0.83 0.43 

AgNOa 28.0 0.83 0.36 

NH^NOg 28.0 0.86 0.39 

KI 42.0 0.94 0.62 

The values of Ao are not given in this table, but they will be found in 
Table XXII. By means of the constants in these tables the equivalent 
conductances of the various electrolytes may be calculated at any de- 
sired concentration within the limits of experimental error up to approxi- 
mately normal concentrations. It is obvious that a comparison of the 
ionization of different electrolytic solutions may be made by means of 
the constants given above. The relative ionization of two salts will vary 
as a function of the concentration, since the constants for the two elec- 
trolytes will not, as a rule, have the same value. The values of the 
constant K have already been considered and need not be further dis- 
cussed here. The values of the constant D are seen to lie within fairly 
narrow limits. Excepting the constants for potassium amides and silver 
iodide, the values of D lie between 0.127 and 0.62, and most of the 
values lie between 0.24 and 0.43. There is no fixed relation between the 
values of D and of K, although in general an electrolyte with a large 
value of K has a large value of D. Thus, potassium amide, silver iodide 
and ammonium chloride have the smallest values of K and likewise they 
have the smallest values of the constant D. So, also, potassium iodide, 
which has the highest value of the constant K, likewise has the highest 
value of the constant D. Apparently, the constants K and D are not 



74 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

entirely independent of each other, or, in other words, they depend in 
a corresponding manner upon some property of the electrolyte. The 
values of m lie between 0.70 and 1.18 and, for the most part, they lie 
between 0.82 and 0.96. The general form of the curve, as we shall 
presently see, is determined largely by the value of the constant m. It 
follows, consequently, that the curves for the various electrolytes will in 
general be similar. No definite relation appears to exist between the 
values of the constant m and the constants D and K. In many cases, 
however, as we shall see later, electrolytes having a small value of K 
and D have a relatively large value of m. Silver iodide is an exception 
to this rule. 

The constants for a number of organic electrolytes are given in 

Table XXVIII. 

TABLE XXVIII. 

Constants of Equation 11 fok Obganic Electeolytes 
IN NH3 AT —33°. 

Solute A„ 10* X m D 

Cyanacetamide 260 0.045 1.24 0.026 

Benzenesulphonamide 208 1.39 1.00 0.029 

Methylnitramine 256 8.4 0.85 0.080 

Metanitrobenzenesulphonamide 231 12.5 0.76 0.103 

Nitrourethaneammonium 262 21.6 0.76 0.22 

Trinitraniline 234 30.0 0.73 0.38 

They have been arranged in the order of increasing values of K. It is 
at once evident that there is no relation between the various constants 
and the value of Ao. On the other hand, there is apparently a rough 
parallelism between the constants K and D. The order of the K and D 
constants, in other words, is identical. The order of the constant m 
appears to be the reverse of that of the constants D and K; that is, as 
K and D increase, m decreases. 

Aside from solutions in liquid ammonia, the equation has been found 
to hold for solutions in sulphur dioxide,^ amyl and propyl * alcohols and 
phenol.* In the case of the sulphur dioxide solutions the equation holds 
within the limits of experimental error. In that of the alcohol solu- 
tions, the deviations appear to be considerable at certain points, but it is 
possible that these are due either to experimental errors or to a lack of 
proper adjustment of the constants. The constants found are as follows: 

' KrauB and Bray, loc. cit. 

•Keyes and Wlnninghoft, J. Am. Chem. Soo. S8, 1178 (1916). 

•Kurtz, Thesis, Clark DnlTeralty (1921). 



FORM OF THE CONDUCTANCE FUNCTION 75 

TABLE XXIX. 

Constants of Equation 11 for Solutions in Different Solvents. 

Solvent Solute m K D Ao 

Sulphur dioxide KI 1.14 8.5X10"* 0.403 207. 

Iso-amyl alcohol Nal 1.2 5.85 X 10"" 0.374 7.79 

Propyl alcohol Nal 0.75 38.3 X lO"'' 0.208 20.1 

Phenol (CH3)^NI 1.28 2.3X10"* 0.69 16.67 

Comparing the ionization in ammonia and sulphur dioxide, in view 
of the much lower value of the constant K, dilute solutions in sulphur 
dioxide are ionized to a much smaller extent than are solutions in am- 
monia. On the other hand, in the more concentrated solutions, the ioniza- 
tion values again approach each other, since the value of D for sulphur 
dioxide is relatively large and the value of m is much greater than that 
in ammonia. The conductance curves of solutions in sulphur dioxide, 
phenol and amyl alcohol pass through a minimum while that of solu- 
tions in propyl alcohol resembles the curve for aqueous solutions. 

In the case of a great many solutions whose ionization is relatively 
low, the limiting value of the equivalent conductance in dilute solutions 
cannot be determined. Under these conditions, the value of K remains 
indeterminate. Nevertheless, if the ionization is relatively low, the ap- 
plicability of Equation 11 may be tested approximately. It is apparent 
that, when the ionization is low, the constant K becomes negligible in 
comparison with the term involving the constant D. Also, the value 
of A becomes small in comparison with that of Ao, so that for purposes 
of approximation the value of A may be neglected in comparison with 
that of Ao. Under these conditions Equation 11 reduces to the form: 

(12) CA== = DAo2 — ™ (CA)^. 
For the sake of brevity we may write: 

(13) I»Ao2-™=P. 

If we take the logarithm of both sides of this equation, we obtain the 
linear equation: 

(14) log CA= = m log CA + log P. 

In order to test the applicability of the equation to solutions of very low 
ionization, therefore, it is only necessary to plot the logarithms of the 
values of CA and of CA^ both of which may be obtained from experi- 
mental data. If the equation holds, the points will lie upon a straight 



76 



PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



line, the slope of which gives the value of the constant m and the inter- 
cept on the axis of CA^ the value of P. 

In Figure 12 are shown plots of Equation 14 for a number of organic 
electrolytes dissolved in hydrobromic and in hydriodic acids and in 




2.5 '-o 

Log(eA) 

Fig. 12. Illustrating the Applicability of Equation 11 to Solutions of Binary Elec- 
trolytes in Solvents of Low Dielectric Constant. 

hydrogen sulfide. These solutions are well adapted to the purpose of 
testing the applicability of the equation, since the ionization of electro- 
lytes in these solvents is extremely low. It is evident that, except in the 
case of a few very concentrated solutions, the equation holds within the 
limits of experimental error. The curves, in general, have approximately 



FORM OF THE CONDUCTANCE FUNCTION 77 

the same slope, which follows from the fact that the value of m is ap- 
proximately the same for these solutions. The greater the value of the 
exponent m, the steeper the curve on the plot. A great many solutions 
of this type have been measured and the results have been compared 
with the equation. The deviation in no case appears to be very great, 
from which it may be concluded that the equation holds to a considerable 
degree of approximation. The values of the constants m and P for 
various solutions are given in Table XXX." 

Many of the substances which appear in this table are not ordinarily 
classed as typical electrolytes. They are, in general, basic compounds 

TABLE XXX. 

Values of the Constants of Equation 12 for Various Solutions. 
Liquid Hydrochloric Acid (HCl). 

Tempera- 
Solute Formula ture m P 

Triethylammonium chloride (C,H,)3N.HC1 —100° 1.42 5.75 

Acetamide CH3CONH, —100° 1.40 5.53 

Methylcyanide CH3CN —100° 1.44 4.17 

Resorcinol CeH,(OH), -89° 1.18 3.89 

Hydrocyanic acid HCN —100° 1.46 3.33 

Toluic acid CH3 . CeH.COOH - 96° 1.52 1.58 

Diethylether (C,H,) ,0 - 100° 1.51 1.38 

Propionic acid C,H,COOH - 96° 1.47 1.21 

Acetic acid CH3COOH - 96° 1.42 1.09 

Benzoic acid CH.COOH - 96° 1.42 0.94 

Butyric acid C3H,C00H - 96° 1.45 0.85 

Methylalcohol CH3OH - 89° 1.61 0.71 

Formic acid HCOOH - 96° 1.55 0.67 

Ethylalcohol C,H,OH -89° 1.70 0.50 

Butylalcohol CAOH -89° 1.62 0.38 

Liquid Hydrobromic Acid (HBr). 

Triethylammonium chloride f^H.hN.HCl -81° 1.51 4.03 

Thymol SS^p?f^^- ''^ 8?° 153 248 

Methylcyanide Sg^^ni^x. "rJo {-g 2 29 

Acetamide '^^fP^^' "Via Al fss 

Aretone (CH3 ^CO —81° 1.63 1.88 

Metacresol m-CH3.CeH,0H -80° 1.54 1.70 

Soni"oto-lu;ne-::: o-CH;;ChM -Jr 1.50 0.99 

Benzoic acid C«H,COOH -80° 1.67 0.82 

Acetic acid CH3COOH -80° 1.66 0.78 

10 Eraus and Bray, Joe. cit. 



78 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



TABLE XXX.— Continued. 

Liquid Hydrobromic Acid (HBr). 

Tempera- 
Solute Formula ture 

Metatoluic acid m-CH, . CeH.COOH — 80° 

Paratoluic acid p-CH, . CeH.COOH — 80° 

Butyric acid C^H.COOH — 80° 

Orthotoluic acid o-CH3CeH,COOH — 80° 

Diethylether (C.HJ^O —81° 

Paracresol p-CHs.CeH.OH —80° 

Resorcinol CeH.lOH)^ —80° 

Orthocresol o-CHg.CeH.OH —80° 

Methylalcohol CH3OH —80° 

Allylalcohol C^Hj-CH^OH —80° 

Ethylalcohol C^H^OH — 80° 

Amylalcohol C^HiiOH —80° 

Normal propylalcohol n-CaH.OH — 80° 

Phenol CeH^OH —80° 

Liquid Hydriodic Acid (HI). 

Triethylammonium chloride (C2HJ3N.HCI —50° 

Ethylbenzoate CeH^COOCjHB —50° 

Diethylether {O^B.^)Jd —50° 

Liquid Hydrogen Sulfide (HjS). 

Triethylammonium chloride (C^HJaN.HCl —81° 

Nicotine CioHi^N^ —81° 

Mercuric Chloride (HgClJ. 

Caesium chloride CsCl 282° 

Potassium chloride KCl 282° 

Ammonium chloride NH^Cl 282° 

Sodium chloride NaCl 282° 

Cuprous chloride CuCl 282° 

Liquid Iodine (I2). 
Potassium iodide KI 140° 

Ethylamine (C^H.NHJ. 

Silver nitrate AgNOg 0° 

Ammonium chloride NH^Cl 0° 

Lithium chloride LiCl 0° 

Amylamine (C^HiiNHJ. 
Silver nitrate AgNO^ 25° 



m 



1.65 


0.77 


1.62 


0.76 


1.66 


0.71 


1.60 


0.65 


1.63 


0.59 


1.66 


0.55 


1.40 


0.52 


1.68 


0.45 


1.80 


0.41 


1.79 


0.39 


1.80 


0.35 


1.84 


0.27 


1.77 


0.27 


1.61 


0.27 


1.58 


2.69 


1.62 


2.09 


1.66 


1.26 


1.58 


2.06 


1.63 


1.20 


1.20 


14.5 


1.21 


14.3 


1.22 


14.3 


1.29 


13.7 


1.33 


13.6 


1.44 


13.5 


1.42 


4.68 


1.57 


1.97 


1.54 


1.80 


1.67 


1.97 



FORM OF THE CONDUCTANCE FUNCTION 79 

TABLE XXX.— Continued. 

Aniline (C,H,NH,). 

Tempera- 

feolute Formula ture m P 

Ammonium iodide NH^I 25° 1 44 2 19 

Silver nitrate AgNOj 25° 142 202 

Pyridine hydrobromide C^H^N.HBr 25° 151 191 

Aniline hydrobromide CeH.NH^.HBr 25° 1.44 129 

Lithium iodide Lil 25° 1.33 l!o4 

Methyl Aniline (CeH^NHCHj). 

Pyridine hydrobromide CgHgN.HBr 25° 1.64 1.19 

Aniline hydrobromide CeH^NH^.HBr 25° 1.59 0.59 

Acetic Acid (CH^COOH). 

Lithium bromide LiBr 25° 1.43 2.60 

Pyridine CsH^N 25° 1.56 1.86 

Dimethylaniline CeHBNCCHa)^ 25° 1.48 1.53 

Aniline CeH^NH^ 25° 1.52 1.32 



Propionic Acid (C^HgCOOH). 

Lithimn bromide LiBr 25° 1.74 0.84 

Aniline CeHgNH^ 25° 1.79 0.37 

Pyridine CsH^N 25° 1.76 0.32 

Bromine (Bt^) . 

Trimethylammoniumchlo- 

ride" (CH3),NHC1 18° 1.62 0.55 

Iodine" I^ 25° 1.74 0.17 

containing either oxygen or nitrogen and in all likelihood they owe their 
electrolytic properties to the formation of complexes with the solvent, 
in which oxygen and nitrogen exhibit basic properties. For a given 
value of TO the ionization is in general the greater the greater the value 
of P. It is apparent that among these electrolytes the typical salts are 
the most highly ionized. In solutions in the halogen acids and hydrogen 
sulphide, the substituted ammonium salts, or their derivatives, are more 
highly ionized than are other substances. In general, also, the typical 
salts have values of the constant to smaller than those of electrolytes 
which have a lower ionization. There are, however, a few exceptions, 
such, for example, as resorcinol in hydrochloric acid, which has a value 

"Darby, J. Am. Ohem. Soc. iO, 347 (1918). 

"Plotnjkow a|i4 Epkotjan, Zfsphr. /. phys- Cheiti. S^, 365 (1913). 



80 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

of m of only 1.18. Correspondingly, resorcinol in hydrobromic acid has 
a constant of only 1.40, which is distinctly lower than that of other sub- 
stances dissolved in this solvent. It is interesting to note that the value 
of the constant m never exceeds 2. The highest value of this constant is 
1.80 for methyl and ethyl alcohols in hydrobromic acid. It appears prob- 
able that the values of m for these two substances in hydrogen iodide 
will be found greater than in hydrogen bromide. 

In fused mercuric chloride the different typical salts exhibit a very 
similar behavior. The constant P differs only inappreciably for different 
electrolytes and the values of the constant m, for the most part, fall 
within very narrow limits. 

In the amines the constant m increases and the constant P decreases 
as the organic radical becomes more complex. The same is true in the 
case of acetic and propionic acids, where the constant m for propionic 
acid is much greater than for acetic acid. Judging by the relatively low 
value of the constant m for liquid iodine, this substance is a fairly good 
ionizing agent. 

2. Geometrical Interpretation of the Conductance Function. The 
conductance function: 



may be interpreted most readily by graphical methods. It will be under- 
stood that Y = V— and that the following equations may at once be con- 

verted to equations in which CA and A appear as variables in place of 
Cy and y. In speaking of the ionization, it is not intended to convey the 
impression that the conductance ratio necessarily measures the ioniza- 
tion, but rather it is introduced as a convenient variable for the purpose 
of discussion. If we differentiate the above equation, we have: 



(15) 



dy _ Y' fCy dK 



d(CY) 



_ y-'(Cy AK' \ 

~K'\K' A(Cy) J- 



dv 

The coefficient ,' , which is the tangent to the y, Cy-curve, is a 

measure of the change of the ionization as a function of the ion concen- 
tration at any point on the curve. It is evident that if the term 

K' d(C ) ^PP^'^^^^^s zero as Cy approaches zero, the tangent will ap- 
proach the value — -= as a limit, where K is the limit which K' ap- 



FORM OF THE CONDUCTANCE FUNCTION 81 

proaches at zero concentration. At higher concentrations the tangent 
will decrease ; that is, the ionization will increase less rapidly for a given 

increase in the ion concentration, because both K' and -— , ,^ , in- 

K' d(Cy) 

crease with the concentration. 

If we introduce A and CA as variables. Equation 15 has the form: 

Hfi^ dA _ A' fCA dK' \ 

^ ' d(CA)~Ao=K' Vi^' d(CA) ^ J' 

The plot of A against the specific conductance in dilute solution will 
therefore be a curve convex toward the axis of specific conductances, and 
as the concentration decreases it will approach a line whose tangent is 

— -=r, provided the conditions mentioned in the preceding paragraph are 
li. 

fulfilled. 

In order to follow up the form of the curve at higher concentrations, 

we may introduce the conductance function 11. On differentiating this 

function we have: 

dA A^ / 1 "^-K \ 

Since K' approaches K at low concentrations, it follows that the tangent 

approaches the value — -= as a limit. At higher concentrations, the 

tangent decreases, since K' decreases. Ultimately the form of the curve 
depends upon the value of m. If m is less than 1, then the tangent will 
always have a negative value; in other words, the equivalent conduct- 
ance will always decrease with increasing values of the specific con- 
ductance. On the other hand, when m is greater than unity, the tangent 
will become zero, when: 

, mK „ 
(18) m — 1 ^=0; 

that is, at this point the conductance passes through a minimum value 
after which it increases with increasing values of the specific conduct- 

(CA\™ 
-^1 + K, and denotmg by C 

and A' the values of the concentration and the equivalent conductance at 
the minimum point, we have: 






82 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

where y' =-^. This equation gives the value of the specific conductance, 

° 
or the ion concentration, at the minimum point. The value of the ioniza- 
tion follows from the equation: 

(20) ^^_ DiCr)+K 

When m equals 1, we have a limiting case in which Equation 18 reduces 
to: 

dA A" mK 



(21) 



d(CA)~Ao^X' K' 



It is evident that since -=7 decreases as the concentration increases, the 

tangent approaches a value zero at high concentration. The ionization, 
therefore, approaches a constant value which may be obtained by writing 
m = 1 in Equation 11; we have: 



or, neglecting K, 



Cy"Y±Yr^D{CY')+K 

D 



(22) T^-zr, = D or 



1 — Y"~ ' 1 + D' 

The ionization of such solutions, therefore, approaches the value 



1+D 

as a limit. If an electrolyte has a very small value of K and a relatively 
large value of D, while the value of m is nearly unity, the conductance 
will vary only very little with concentration at higher concentrations. 
This is the case with the cyanides in liquid ammonia, more particularly 
with the cyanides of gold and silver. The value of m is a little less than 
unity for the first substance and a little greater than unity for the 
second.^^ For the ion concentration Cy = 1, Equation 11 reduces to: 

:j^^i— =D + K, 
1 — Yi 

and since K may be neglected at this concentration, we have: 

(23) ~^^^ = D. 

1 — Yi 

The constant D, therefore, measures the ratio of the ionized to the un- 
ionized fraction at the concentration Cy = 1. We shall see that, for a 

" Kraus and Bray, loc. cit., p. 1360. 



FORM OF THE CONDUCTANCE FUNCTION 83 

given substance in different solvents or in the same solvent at different 
temperatures, the value of D is practically constant, while the values of 
m and K vary. It follows, therefore, that the y, Cy-curves for all such 

solutions pass through the point Cy = 1, Y = Tviri • '^'^^^ relation is of 

importance in interpreting the influence of temperature on the conduct- 
ance of solutions. 

The further discussion of the relation between the conductance and 
the concentration is greatly simplified by introducing the function K' and 
examining the manner in which K' varies as a function of the ion concen- 
tration. Differentiating, we have the equations: 

-1 



dK' Dm(CA) 



m'- 



(24) or 



d(CA) A w* 

= Dm(Cy) 



dK' ^„,^ .m-= 



d(CY) 

If D were zero, that is, if the mass-action law held, we should have: 

dK' 

(25) dicrr^ 

or K' = constant. 

On the other hand, when the D term is present, K' will always increase 
with the concentration. The form of the K', CA-curve is determined 
mainly by the constant m. When m = 1, we evidently have: 

(26) dTCY)=^" °' d(CA) = ]^- 

In this limiting case, therefore, K' varies as a linear function of the 
specific conductance CA. 

The form of the curves for values of m greater and less than unity 
may readily be determined by means of the second differential coefficients. 
We have: 

(27) H?i.=i^-(— 1)(^Y)-^ 



d(CY) = 

d^K' 



When TO < 0, 

<o 



(28) dlCyP 

and the K, Cy-curve is everywhere concave toward the axis of Cy. When 

m > 1, 



84 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

and the curve is everywhere convex toward the Cy-axis. In the limiting 
case, m = 1, and 

(30) d(C^ = 0, 

and £ is a linear function of Cy. 

From Equation 24, it follows that when m < 1, 

dK' 

(31) ^i- d(CA)= =° 
and when m > 1, 

(32) „!l^di&)=0. 

In the first case the K', Cy-curve approaches the limit K asymptotic 
to the axis of K', while in the second case it approaches the limit 
asymptotic to a line parallel to the axis of Cy. 

The curvature of both curves increases as the concentration de- 
creases.^* For the radius of curvature of the K', Cy-curve we have the 
equation: 

2(2-m) 2(2m-i) 

(66) ti —[Dm{m—l)Y/^ "•" {m—iy^ 

The exponent 2— m of the first term of the right-hand member of this 
equation is positive for all values of m less than 2. Since no solutions 
are known for which m is greater than 2, we need not consider greater 
values of m. It is evident, therefore, that, due to the first term, the 
radius of curvature increases with Cy for all values of m. For m > 1, the 
coefficient 2m — 1 is positive and the radius of curvature increases with 
Cy due to this term also. When m < 1, 2 — m > 2m — 1 so long as m is 
greater than zero. It follows, therefore, that the first term overbalances 
the second and that the curvature, for all values of m between zero and 2, 
decreases with increasing concentration, becoming infinite in the limit. 
For m = 1, jB = oo, and the curvature is zero. For m < 1, the curvature 
is negative ; that is, the curve is concave toward the Cy-axis. While for 
m > 1, the curvature is positive, and the curve is convex toward this axis. 
For given values of D and K and for different values of m we have a 
family of curves passing through the points Cy =^ Q, K' ^ K and Cy = 1, 
K' = D -\- K. Such a system of curves is shown in Figure 13. The con- 

"Kraus, J. Am. Chem. /Sfoo. i2, 6 (1920). 



FORM OF THE CONDUCTANCE FUNCTION 



85 



stants assumed are: D = 1.703, K = 0.001, and Ao = 129.9 for all curves, 
while m = 0.52 for Curve I, m = 1.50 for Curve II, and m = 1 for Curve 
III. The greater the value of m, the less rapidly does K' increase at the 
lower concentrations. For a value of m = 0, the curve degenerates into 
a horizontal straight line, corresponding to the mass-action constant 
K' = K + D. 

1.8 



1.6 



1-4 



?.„ 



^ 
^ 



o,8 



0.6 



0.4 





















^ 
















^ 


^/ 


/ 














^ 


/ 


/ 










runiy 


/ 




/ 


A 










/ 


/ 


cimvtni/ 


/ 


/ 










/ 


/ 


/ 


/ 


/btnti 










/ 


/ 


/ 


/ 


/ 










' 


/ 


/ 




y 














'^ 


7^ 


X 

















o.o 



0.2 0.3 0.4 0.5 0.6 

Ion Concentration (Cv). 



0.7 0.8 09 



Fig. 13. Showing Typical K' Curves for Different Values of m According to 

Equation 11. 

It is evident that a given percentage deviation of K' with respect to 
K will be found at different values of the ion concentration. If we con- 
sider two solutions for which the value of K' has increased by a given 
percentage amount over K in both cases, then the ion concentrations of 
the two solutions are related according to the equation: 

P. 

If BJK for the two solutions is of the same order, then the ratio of 
the ion concentrations will depend upon the values of m. The smaller 
the value of m, the lower will be the ion concentration at which a given 
change in K will be found. This is also obvious from Figure 13. For 



(34) 



86 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

a given rise in the curve above the value of K, the ion concentration will 
be the smaller, the smaller the value of m. The value of the ion concen- 
trations corresponding to any given value of K' are found by drawing a 
horizontal line and reading off the concentrations at the points of inter- 
section. In Table XXXI are given the values of m, D/K, and the ion 

TABLE XXXI. 

Value of D/K and of m and Concentrations at Which Given Devia- 
tions FROM THE Mass-Action Law Occur for Solutions in NHg. 



Electrolyte D/KXW" rn ^^-^--=5% =^=20% 



K'-K_.„ K'-K_ 

CtXIO' CXIO' C7XIO' cxio* 

KNH, 7.91 1.18 2.76 8.82 8.97 65.0 

Agl 0.345 0.70 0.86 1.14 6.38 18.03 

NH.CI 1.06 0.84 1.10 1.19 5.70 7.99 

KNOo 1.35 0.89 1.35 1.46 6.89 10.80 

NaNOj 1.39 0.89 1.33 1.42 6.52 8.06 

NH^Br 1.04 0.82 0.89 0.92 4.85 5.70 

LiNO. 1.31 0.86 1.06 1.10 5.33 6.32 

Nal 1.54 0.83 0.63 0.64 3.33 3.66 

AgNO, 1.29 0.83 0.78 0.80 3.38 3.80 

NH.NO. 1.39 0.86 0.98 1.02 4.92 5.64 

KI 1.43 0.94 2.03 2.12 8.91 10.50 

Cyanacetamide 55.8 1.24 0.83 15.4 2.53 120.0 

Benzenesulphonamide 2.09 1.00 2.40 6.34 9.59 64.8 

Methylnitramine 0.941 0.85 1.32 1.52 7.08 12.04 

Metanitrobenzenesulphonamide 0.825 0.76 0.58 0.61 3.62 4.49 

Nitrourethaneammonium 1.02 0.76 0.44 0.45 2.74 3.03 

Trinitraniline 1.27 0.73 0.22 0.22 1.45 1.49 

concentrations Cy and the total salt concentrations at which the increase 
over the values of K amounts to 5 and 20 per cent respectively. 

For approximately the same value of D/K the value of Cy, for which 
a given increase occurs in the value of the mass-action function, decreases 
as m decreases. Thus, in the case of benzenesulphonamide, methyl- 
nitramine, metanitrobenzenesulphonamide, and trinitraniline, the value of 
m decreases from 1.0 to 0.73, while the value of Cy for a 5% increase in 
the function decreases from 2.40 to 0.22. Similarly, in the case of sodium 
and potassium iodides, the values of m are respectively 0.83 and 0.94, 
and the values of the ion concentrations for a 5% increase in the func- 
tion are 0.63 and 2.03 respectively. The deviations from the simple 
mass-action law, at a given concentration therefore appear smaller in the 
case of potassium iodide than in that of sodium iodide. For the same 



FORM OF THE CONDUCTANCE FUNCTION 87 

value of the constant m, a given deviation occurs at the lower concen- 
tration, the greater the value of D/K. Thus, sodium iodide and silver 
nitrate both have a value of the exponent m = 0.83, while the values of 
D/K are 1.54 and 1.29 respectively. Correspondingly, the values of the 
ion concentrations for a 5% increase of the function are 0.63 and 0.78 
respectively. The value of D/K for typical electrolytes in ammonia lies 
in the neighborhood of 100. For weak electrolytes the value of D/K 
appears to be larger, as for example for cyanacetamide and potassium 
amide. In the case of silver iodide, however, which appears to be a very 
exceptional electrolyte, the value of D/K is extremely small. As we shall 
see below, the value of D for a given electrolyte is relatively independent 
of the nature and condition of the solvent. At higher temperatures, the 
dielectric constant of the solvent decreases and with it there is a large 
decrease in the value of the constant K, while the constant D remains 
practically fixed. At higher temperatures, therefore, the value of D/K 
will increase. This tends to increase the deviations from the simple 
mass-action relation. On the other hand, the value of m increases with 
increasing temperature and decreasing dielectric constant, and this tends 
to make the percentage deviations from the simple mass-action relation 
smaller. The observed effect will be the resultant of these two. From 
the known form of the conductance curve in solvents of very low dielec- 
tric constant, it is evident that ultimately the effect due to the increase 
in the value of D/K overbalances that due to the increase in the 
value of m. 

Corresponding to the K', Cy-curves, we have the y, Cy-curves. These 
curves pass through the common points y ^ 1, Cy = 0, and y =: 

D + K ,„ , 

j-^-^^-^andCY = l. 

The particular case when the value of m is equal to unity, which 
leads to a linear relation between the function K' and the ion concentra- 
tion, likewise yields a very simple relation between the equivalent con- 
ductance and the specific conductance. In this case we may write our 
equation: 

' -D + ^ 



1-Y ^ ' Cy 
(35) or ^ = D + ^. 
It is obvious that the ratio -» ^, or what is proportional to it, the ratio 

— - — is now a linear function of the reciprocal of the specific conduct- 
1-y 



88 .PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ance or of the ion concentration. The equation obviously approaches in 
form that which follows from the mass-action law which is: 

(36) -^^ = ^. 

1 — y Cy 

If the mass-action law holds, the ratio of the ionized to the un-ionized 
fraction is inversely proportional to the ion concentration. If, therefore, 

we were to plot the values of the ratio ■— — against values of the ion 

1-Y 

concentration Cy, we should obtain a rectangular hyperbola. When the 

constant m equals unity, the equation is of the same form, except that 

the entire curve is raised by an amount equal to D. In this case, there- 

Y 
fore, the curve is again a rectangular hyperbola asymptotic to the -— — — 

Y 
axis on one side and asymptotic to the horizontal line y— — ^ D on the 

other. 

In very concentrated solutions, in the case of substances for which the 
value of m does not differ too greatly from unity, the equivalent con- 
ductance at a given concentration for different electrolytes is roughly 
proportional to the value of D. The value of this constant, as has already 
been pointed out, is in a large measure a distinctive property of the 
electrolyte and varies only little as a function of the solvent. For the 
strongest electrolytes the value of D is always of the same order. 

As we shall see later, the conductance of an electrolyte is a function 
of the temperature. At very high and very low concentrations the con- 
ductance invariably increases with increasing temperature, while, at in- 
termediate concentrations, the conductance in many cases decreases with 
increasing temperature, and always decreases at high temperatures. As 
we shall see, this behavior is due to the fact that the value of D remains 
constant and independent of the temperature, while the constant m 
varies, increasing with increasing temperature. At intermediate concen- 
trations, therefore, the ionization decreases with increasing temperatures 
whereas at very high and very low concentrations the ionization remains 
practically fixed. 

3. Relation between the Properties of Solvents and Their Ionizing 
Power. Various attempts have bfeen made to connect the power of a 
solvent to ionize dissolved substances with the properties of this solvent. 
So, for example, it has been suggested that those solvents which are 
normally associated are capable of dissociating substances dissolved in 
them. This relation, however, is not a general one for it is now known 



FORM OF THE CONDUCTANCE FUNCTION 89 

that all liquid substances are capable of ionizing substances dissolved in 
them quite irrespective of what their properties may be. The only con- 
dition necessary in order that the solution shall conduct the current is 
that the electrolyte shall be sufficiently soluble so that a highly concen- 
trated solution may be obtained. We have seen, in the preceding section, 
that in solvents which have a low ionizing power the conductance de- 
creases with decreasing concentration, and appears to approach a value 
of zero. If the electrolyte, therefore, is not very soluble, its influence on 
the conductance of the solvent will be inappreciable. If, however, an 
electrolyte is soluble up to concentrations as high as normal, then its 
solutions will in all cases be found to conduct the current. In general, 
the typical inorganic electrolytes are not soluble in weak ionizing agentS) 
but certain organic electrolytes, such as the salts of organic bases, are 
quite soluble and yield solutions which conduct the current. It is prob- 
able that all liquid dielectric media to some extent possess the power of 
ionizing substances dissolved in them. 

The difference between the properties of solutions of electrolytes in 
different solvents does not consist in a power to ionize an electrolyte jn 
one case and the entire absence of this power in another, but rather in 
a difference in the form of the conductance curve which varies with the 
nature of the solvent, either with its constitution or with its temperature. 
That property of the solvent which appears to control the form of the 
conductance curve is the dielectric constant. Thomson " and Nernst ^° 
first suggested that the ionizing power of a solvent is determined by its 
dielectric constant. This constant, however, is by no means to be taken 
as a measure of the ionizing power of a solvent, for the ionization curve 
of a given electrolyte is a complex function of the concentration and the 
relative ionizations will vary with the concentration. At very high con- 
centrations the relative ionizations will, in general, differ much less than 
at low concentrations. Indeed, in the preceding section we saw that the 
constant D determines the ionization at very high concentrations and 
that, therefore, for a given electrolyte in different solvents there is a 
certain concentration at which the ionization of this electrolyte will be 
practically the same in all solvents. What we must expect to find, there- 
fore, is that the form of the conductance curve is determined by the 
dielectric constant of the solvent. The relation between the conductance 
and the dielectric constant is therefore shown most readily by bringing 
out the relation between the constants of the conductance function and 
the dielectric constant. In the following table are given values of the 



"Thomson. PMl. Mag. [5] S6, 320 (1893). 
"Nernst, Zt3chr. f. phys. Chem. IS, 531 (1894). 



90 



PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



dielectric constant and the constants m, D, and K for electrolytes in 
different solvents. So far as possible, typical electrolytes have been 
chosen, since, as we have seen, the constants are in general a function of 
the electrolyte. We have seen, however, that the typical electrolytes be- 
have similarly in a given solvent, so that a rough comparison may be 
made between the dielectric constant and the various constants which 
determine the form of the conductance function. Those values of D 
which appear in parentheses have been calculated from the values of P, 
assuming that the value of A„ is proportional to the fluidity of the 
solvent. This relation is not strictly true, particularly in the case of the 
inorganic solvents. However, it unquestionably gives the order of mag- 
nitude of this constant. 



TABLE XXXII. 

Constants op Equation 11 and Dielectric Constants for Various Solvents. 

Dielectric 

Solvent Solute constant m D KXIO* 

Hydriodio acid (C2H5)3N.HC1 29 1.58 (0.58) 

Amylamine AgNOs 4.5 1.67 

Propionic acid LiBr 5.5 1.74' (0.30) 

Methylaniline C.HsN.HBr 5.9 1.64 

Ethylamine AgNOs 6 2 1.45 (0.22) 2.4X10-* 

Ethylamine NH.Cl 6.2 1.57 

Hydrobromic acid (C2H5)3N.HC1 6.3 1.51 (0.54) 

Aniline AgNOa 7.5 1.42 (0.44) 

Aniline NHJ 7.5 1.44 (0.51) 

Hydrochloric acid (C2HB)aN . HCl 9.5 1 .42 (0.39) 

Acetic acid LiBr 9.7 1.43 (0.30) 

Phenol (Ca)4NI 9.7 1.28 0.69 2.8 

Hydrogen sulfide (&Hb)3N . HCl 10.0 1.58 (0.30) 

Methylamine AgNOs 10.0 1.22 0.30 0.80 

Ethylenechloride (C3H,)4NI 10.5 . . 1.45 

Pyridine Nal 12.4 . . 13.0 

Pyridine KI 12.4 . . 5.2 

Acetoaceticester NaSCN 15.7 . . 9.5 

Isoamylalcohol Nal 15.9 1.2 0.403 5.85 

Isoamylaleohol Lil 15.9 .. 73 

Acetophenone Nal 16.4 .. ..'.." 34.0 

Sulfur dioxide KI 16.5 1.14 0.40 85 

Methylethylketone Nal 18.4 .. 23.0 

Isobutylalcohol NaT 18.9 . . 12 

Acetone Nal 21.8 .. 39 

Ammonia Nal 22.0 0.83 0.43 28 

Ammonia AgNOa 22.0 0.83 0.36 28 

Epichlorhydrin (CzHb),^ 22.6 .. 485 

Propylalcohol Nal 23.0 0.75 0.208 383 

Benzonitrile Nal 26.0 .. 55.0 

The solvents are arranged in the order of their dielectric constants. 

It will be observed, in the first place, that the constant D is in all cases 
of the same order, varying between 0.2 and 0.69 with a mean value in the 



FORM OF THE CONDUCTANCE FUNCTION 91 

neighborhood of 0.4. This constant, therefore, is a characteristic prop- 
erty of the electrolyte upon which the solvent has only a secondary influ- 
ence. In this connection, it is to be borne in mind that various com- 
plexes may be formed between an electrolyte and its solvent, upon the 
nature of which complexes the constant D may depend. We should 
therefore expect a certain amount of variation in the value of the con- 
stant D for a given electrolyte in different solvents. Probably the change 
in the value of D would be found to be much smaller in case the dielectric 
constant were altered, not by a change of the solvent medium, but by a 
change of the temperature. The constant m is seen to decrease as the 
dielectric constant increases. Since this constant is a property of the 
electrolyte, as well as of the solvent, it follows that an exact comparison 
cannot be made. However, it is clear that, for solvents of very low 
dielectric constant, the value of m approaches 2, whereas for solvents 
of very high dielectric constant the value of m is less than unity. In 
the case of water m appears to have a value in the neighborhood of 0.5. 
The change in the value of m as a function of the dielectric constant is 
well illustrated in the case of silver nitrate dissolved in the amines. For 
amylamine, ethylamine, aniline, methylamine, and ammonia the dielec- 
tric constants are respectively 4.5, 6.2, 7.5, 10 and 22, and the values of 
m are 1.67, 1.45, 1.42, 1.22 and 0.83. It is seen that throughout this 
series of solvents, which are similar in their constitution, the value of the 
constant m for silver nitrate decreases with increasing values of the 
dielectric constant. 

The mass-action constant K decreases very rapidly as the dielectric 
constant decreases. While there are numerous transpositions in the order 
of the constants, which is to be expected, since this constant is a func- 
tion of the constitution of the salt as well as that of the solvent, never- 
theless, in a general way, there can be no question but that the mass- 
action constant K decreases as the dielectric constant decreases. The 
variation is much more regular when solutions in solvents of the same 
type are compared. So, in the case of solutions of silver nitrate in 
ammonia and its derivatives, the constants are as follows: ethylamine, 
2.44 X 10-^ methylamine, 0.8 X 10'*; ammonia, 28 X 10*. When the 
dielectric constant falls below a value of approximately 10, the mass- 
action constant for the typical salts has reached a value in the neighbor- 
hood of 1 X 10"* and thereafter it falls off very rapidly with decreasing 
values of the dielectric constant. No accurate data being available in 
dilute solutions of solvents having a- dielectric constant less than 10, it is 
impossible to proceed further with the comparison. Assuming, however, 
that the conductance function holds, it is possible to calculate the values 



92 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

of the constant K if sufficiently accurate data are available at inter- 
mediate concentrations. The value of K for solutions in ethylamine was 
obtained in this way. The extremely low value of the constant will be 
noted. 

Having shown the relation between the constants of the conductance 
function and the dielectric constant, it will be unnecessary to give a 
detailed list of various solvents which have been found to yield electro- 
lytic solutions. The general form of the conductance curve may at once 
be inferred from the value of the dielectric constant. Many salts are 
not, as a rule, soluble in solvents of low dielectric constant. Neverthe- ' 
less, certain typical salts form solutions with many solvents of very low 
dielectric constant, as for example silver nitrate, which dissolves in amyl 
amine, which has a dielectric constant of only 4.5. Such behavior, how- 
ever, is exceptional and is probably to be ascribed to the formation of 
soluble complexes between the salt and the solvent. Various salts of 
organic bases, however, as has already been stated, are soluble in sol- 
vents of very low dielectric constant. 

The question has been raised as to the influence of the electrolyte on 
the dielectric constant of the medium in which it is dissolved. Walden,^^ 
who has measured the dielectric constants of some non-aqueous solutions, 
concluded that the dielectric constant is greatly increased due to the 
addition of an electrolyte and has suggested that the observed deviations 
of strong electrolytes from the simple mass-action law are due to this 
factor. More recently, however, Lattey ^^ has subjected the methods 
of measuring the dielectric constant of electrolytes to careful examina- 
tion and has himself carried out measurements on numerous aqueous 
solutions. He finds that the dielectric constant of electrolytic solutions 
is considerably lower than that of the pure solvent. For example, for a 
solution of potassium chloride in water of concentration 0.00755 normal 
he obtained the value 66.25 as against 81.45 for pure water. The dielec- 
tric constant diminishes approximately as a linear function of the con- 
centration and the effect for different electrolytes is of the same order 
of magnitude. Further investigations in this direction are much needed. 
The precise form of the functional relation between the dielectric 
constant of the solvent and the ionization of the dissolved electrolyte is 
unknown. Walden^^ has suggested an empirical relation according to 
which the ionization of a typical electrolyte is the same in different 
solvents- when the product of the dielectric constant and the cube root 

1649"(lM3r' ^""' ^'"'^' **■ ^''*'"'^^- "' ^°^ '"•" l'*^^ (1912) ; J. Am. Chem. Soo. S5. 
"Lattey, Phil. Mag. 1,1, 829 (1921). 
"Walden, Ztschr. f. phys. Chem. 5J,, 228 (1905). 



FORM OF THE CONDUCTANCE FUNCTION 93 

of the dilution have the same value. More recently, a number of writers 
have proposed theories of electrolytic solutions which lead to Walden's 
relation as a consequence. Walden has made an extensive study of 
available data ^^ from which he draws the conclusion that his relation 
holds practically without exception. The theories in question will be 
discussed in another chapter. We shall here consider Walden's relation 
from an experimental point of view only. 
In mathematical terms, we have: 



(37) Yi = Y2 = Y3 =, etc. 
then 

(38) e,V,i = 8,7,* = 83F3* = , etc. 

where e is the dielectric constant of the medium and V is the dilution 
of the solution of a given electrolyte, whose ionization fulfills the con- 
dition 37. Walden has tested the relation by comparing the values of 
eF* for solutions of typical electrolytes in different solvents and believes 
to have shown that this quantity is a constant within the limits of experi- 
mental error and minor variations due, perhaps, to differences in the 
condition of the electrolyte in different media. 

It is clear, from Equation 38, that a small variation in the value of 
the product eF* will have as a result a large variation in the resulting 
conductance curve, since the dilution enters as the cube root. Actually 
the variations of the constants are quite large. For example, at an 
ionization of 82%, the product eV* in water has a value of 156, in 
ammonia 286, in isobutylalcohol 333, and in ethylene chloride 315. The 
constancy of the values which Walden has found is in part due to the 
use of unreliable conductance data and in part to the use of Ao values 
which are unquestionably in error. 

It is obvious, according to Equation 38, that, if the ionization curve 
is fixed for a typical electrolyte in one solvent, it is fixed for typical 
electrolytes in all other solvents. For we have, considering solutions of 
a given electrolyte in two different solvents, 

E,F,i = E,F,i, 

(39) or F.= (|)f. 

If F is the dilution in the first medium, at which the ionization of the 
electrolyte is y, then V^, as determined by Equation 39, is the dilution in 

2» Walden, Ztschr. f. phys. Chem. 91,, 263 (1920). 



94 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the second medium at which the electrolyte will have the same ioniza- 
tion. 

In the following table are given values of V calculated according to 
Equation 39, at which the ionization of typical electrolytes is 70% and 
95% in different solvents, based upon an aqueous solution of sodium 
chloride as reference medium. Under Fobs, are given the observed dilu- 
tions at which solutions in the various solvents have the ionization in 
question. 

TABLE XXXIII. 

Observed and Calculated Values of the Dilution V at Which Typical Electeo- 
LYTEs IN Various Solvents Have the Same Ionization. 

Ethyl Epichlor- Aceto- Isobutyl- Ethylene 

Solvent Water Alcohol hydrin phenone Pyridine Ammonia alcohol chloride 

constant . 81.7 25.6 22.6 18.2 13.0 22.0 18.9 10.5 

Ao 108.9 39.42 62.1 33.3 67.0 339.0 12.8 66.7 

Temp 18° 25° 25° 25° 18° —33.5° 25° 25° 

loniz. = 70% : 

Fobs 1-207 125.9 159.1 320.5 861.0 794.5 1348.0 11290.0 

Feaic. 1-207 39.2 56.8 109.0 299.0 61.7 97.5 569.0 

loniz. = 95% : 

Fobs. 181.0 3590.0 3350.0 5970.0 25110.0 11910.0 14620.0 

Fcaic. 181.0 5880.0 8530.0 16300.0 44900.0 9260.0 14600.0 

The electrolyte employed for comparison is sodium iodide, except in the 
case of water, eptchlorhydrin, ethylene chloride and ammonia, in which 
the electrolytes were sodium chloride, tetraethylammonium iodide, tetra- 
propylammonium iodide and potassium nitrate, respectively. So far 
as solutions in water are concerned, the ionization values correspond 
. very closely for different binary electrolytes, so that it is a matter of 
indifference whether one or another typical binary electrolyte is em- 
ployed as reference electrolyte. At the higher concentrations, it is true, 
the value of y is somewhat lower for sodium chloride than for potassium 
chloride. However, this does not affect the comparisons appreciably; 
if anything, the comparison is somewhat more favorable with sodium 
chloride than with potassium chloride as reference electrolyte.. 

If Equation 38 were applicable, the calculated values of V should 
everywhere correspond with the observed values. At an ionization of 
70% the calculated values of V are in all instances too small. The dis- 
crepancy is greatest in the case of ethylene chloride at 70% ionization 
which, according to calculation, should be 569 liters, whereas the meas- 
ured dilution is 11,290. In general, the lower the dielectric constant of 



FORM OF THE CONDUCTANCE FUNCTION 95 

the medium, the greater the discrepancy between the observed and cal- 
culated values, although there are some marked exceptions. Further- 
more, the order of the deviations varies as the ionization of the electro- 
lyte varies. This is particularly noticeable in the case of ammonia and 
isobutyl alcohol, where the observed and calculated values very nearly 
agree at 95% ionization, but diverge largely at an ionization of 70%. 
On the other hand, in other cases, the deviation changes sign. For 
example, at 70% ionization the observed value for ethyl alcohol is 125.9 
and the calculated value 39.2, whereas at 95% ionization the observed 
value is smaller, being 3590, and the calculated value 5880. 

That Walden's relation cannot hold generally may most readily be 
shown by graphical means. If we take logarithms of both sides of 
Equation 39, we have: 

log V, — log Vi= 3 1og^. 

£2 

If the values of y for an electrolyte in different solvents are plotted 
against values of log V, then obviously for any given value of y the 

abscissas on the curves will differ by 3 log — . In other words, the curve 

£2 
for an electrolyte in any one solvent may be derived from that in any 
other solvent by merely displacing the curve along the axis of log V by 

£ 

an amount equal to 3 log — . An inspection of Figure 3, where values 

£2 
of Y for different solvents are plotted as functions of log V, shows at 
once that this condition is not fulfilled, for, if the curve for water were 
displaced parallel to itself, it would not coincide with the curves for 
solutions of typical electrolytes in other solvents, such as ethyl alcohol, 
ammonia and ethylene chloride. Indeed, in order to test the applicability 
of Walden's relation it is not even necessary to know the value of Ao, 

since it follows readily from Equation 39 and from the equation y =-t- 

that if the conductances themselves are plotted as functions of log V, it 
must be possible to derive the curve for an electrolyte in any one solvent 
from that in any other solvent by displacing the curve parallel to itself 
in some direction, this direction being determined by the values of Ao 
and of the dielectric constant e. Those familiar with the properties of 
electrolytic solutions will at once recognize that this condition is not 
fulfilled. 

Actually, it is not to be expected that any simple relation will exist 
between the ionization y and the dielectric constant of the solvent, for, 



96 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

as we have seen, the value of y is expressed approximately as a function 
of the concentration by means of Equation 11. As was pointed out 
above, the constant D is practically independent of the dielectric con- 
stant, while m increases and K decreases with increasing values of this 
constant. As a result, the relative ionization of an electrolyte in two 
solvents will vary with the concentration in a more or less complex 
manner, and in two solvents the order of the ionization values may be 
reversed as the concentration changes. 

The important conclusion to be drawn from the behavior of solutions 
of electrolytes in different solvents is that the conductance function is 
of the same general form in all solvents. A single empirical equation 
is capable of expressing the relation between the conductance and the 
concentration in all cases, practically within the limits of experimental 
error. Whether or not this equation represents precisely the relation 
between the conductance and the concentration is relatively unimportant, 
so long as the deviations from this equation show no decided systematic 
trend. In aqueous solutions, the weak electrolytes follow the mass- 
action law in conformity with the ionic theory. The strong electrolytes, 
however, do not fulfill this condition. It follows from the foregoing con- 
siderations that the conductance curve for strong electrolytes in water dif- 
fers from that of electrolytes in other solvents only as regards magnitude 
of the observed effects and not as regards the nature of the phenomena 
involved. Any theory which has to account for the relation between the 
conductance and the concentration of electrolytes in water must equally 
account for the relation between these quantities in non-aqueous solvents. 

Various theories have been proposed to account for the change of 
the equivalent conductance as a function of the concentration in the case 
of strong electrolytes. The simplest of these is that the degree of ioniza- 
tion is actually measured by the conductance ratio, in which case it is 
necessary to account for the change in ionization as a function of the 
concentration. Unfortunately, a general theory of other than dilute 
solutions does not exist at the present time. A comprehensive method 
of treating concentrated solutions is therefore lacking. The problem of 
equilibrium in a system of charged particles has not been solved, and the 
question therefore remains open as to whether or not the change in 
ionization may be accounted for. On the other hand, the assumption 
may be made that the speed of the ions changes as a function of the 
concentration, as a consequence of which the conductance ratio does not 
correctly measure the degree of ionization. Certain writers have as- 
sumed that typical electrolytes are completely ionized in solution and 
that consequently the change in the conductance is due entirely to a 



FORM OF THE CONDUCTANCE FUNCTION 97 

change in the speed of the carriers. It should be stated, however, in 
this connection, that no theory has thus far been proposed which ade- 
quately accounts for the change in the carrying capacity of the ions as 
a function of the concentration, particularly in solvents of low dielectric 
constant. Any such theory must not only account for an initial diminu- 
tion in the speed of the ions, but it must also account, in many cases, 
for a subsequent increase in the speed with increasing concentration. 
In fact, such a theory must account for the various forms of the con- 
ductance curves in different solvents and for the change in the form of 
the curves as the condition of the solvent is altered. Incidentally, it is 
to be noted that the order of the changes in the speed of the ions on 
this assumption is very great. It is true that, in aqueous solutions, the 
speed does not vary greatly from the most dilute solutions up to normal 
concentration, but in solutions in solvents of low dielectric constant it is 
not only necessary to account for a decrease in speed but in many cases 
for an increase in speed which, over a limited range of concentration, is. 
at times, as great as a thousandfold. It seems very difficult to account 
for a change of speed of this magnitude on the basis of our present 
knowledge of the properties of the carriers in different media. In this 
connection it should be borne in mind that, superimposed on these 
hypothetical changes in the speed of the ions, there is a change due to 
the viscosity of the solution which effect appears in every respect to 
be normal in character. Furthermore, solutions of weak electrolytes, 
both in water and non-aqueous solvents, conform to the mass-action law 
up to fairly high concentrations. If the speed of the ions changes with 
the concentration, then such a simple relation is not to be expected. 

A third hypothesis has been proposed, namely: that the ionization 
reaction differs from that which is commonly assumed. Certain writers 
have made the assumption that, in non-aqueous solutions, the electrolyte 
is associated, the association changing with concentration, and that only 
the associated molecules are capable of ionization. They assume, for 
example, in the simplest case, that the following reactions take place: 

MX 4- MX = (MX) 2 

As the concentration increases, the amount of the polymer increases and 
this increase might be sufficient to provide for an actual increase in the 
number of ions present. If this hypothesis is correct, the current in such 
solutions is carried chiefly by complex ions and consequently transfer- 
ence numbers in such solutions should be abnormal. Reliable trans- 
ference numbers in solvents of low dielectric constant are not available, 



98 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

but from the data for solvents of somewhat higher dielectric constant 
it may be inferred that the transference numbers are approximately 
normal. Furthermore, since it appears that the deviations from the 
mass-action law in aqueous solutions are of the same character as in 
non-aqueous solutions, it follows that similar intermediate ions would 
have to be assumed to be present in solutions of the strong binary elec- 
trolytes in water. If such were the case, not only should the trans- 
ference numbers be abnormal, but they should vary as a function of the 
concentration. Now, while it is true that many transference numbers 
do vary with the concentration, a considerable variation takes place only 
at relatively high concentrations, and only at such concentrations where 
the viscosity of the solution has increased sufficiently to materially affect 
the motion of the ions through the solution. It would seem that trans- 
ference measurements should yield data corroborating this last hypothesis 
if it were correct. So far as available data are concerned, the hypothesis 
is not substantiated. 

4. The Form of the Conductance Curve in Dilute Aqueous Solu- 
tions. The applicability of the conductance function to aqueous solu- 
tions is imcertain. That the Storch equation holds approximately for 
aqueous solutions at higher concentrations has long been known. In 
the case of Equation 11 this would yield for m values of approximately 
0.5, and for D values in the neighborhood of 2. With such large values 
of the constant D and small values of the constant m, it becomes 
very difficult to determine the value of the constant K. At concentra- 
tions sufficiently low, so that the effect of the D term might be neglected, 
the ionization is so nearly complete that it becomes practically impos- 
sible to demonstrate whether or not the mass-action law is approached 
as a limiting form. Kraus and Bray have shown that Equation 11 may 
be applied with considerable exactitude to solutions in water up to 10"' 
normal, provided a value of Ao is chosen which is lower than the experi- 
mentally determined values of the equivalent conductance at very low 
concentrations. More recently, Washburn and Weiland^^ have con- 
cluded from their very accurate conductance measurements on KCl up 
to 2 X 10"° normal that the mass-action law is actually approached as 
a limit. Their results, however, do not appear to be conclusive, since, 
in extrapolating for the value of A„, they assume the mass-action law 
to hold." If the mass-action constant is calculated with a value of Ao 
based on the assumption that the mass-action law holds, then the results 
must necessarily conform to the assumption made. The curve obtained 

"Washburn and Welland, J. Am. Chem. Soc. iO, 106 (1918). 
wpraus, /. Afn, ghejfi. Soc. ifl, 1 (19g0), ' 



FORM OF THE CONDUCTANCE FUNCTION 99 

is Shown in Figure 14, in which values of the mass-action function K' 
are ptotted agamst those of the concentration. The form of this function 
IS entirely different from that which has been found to hold in solutions 
in non-aqueous solvents and it is obvious, moreover, that the function is 
a comparatively complex one. At higher concentrations, and practically 
down to 1.5 X 10- normal, the X', C-curve is everywhere concave 
toward the axis of concentrations. At this low concentration, however, 
the curve changes its form, and approaches a value asymptotic to a line 
parallel to the axis of concentrations. In order to establish the mass- 
action law as a consequence of experimental observations it must be 




Concentration X 10°. 

Fig. 14. Showing Variation of K' with Concentration for Aqueous Solutions of 
KCI at 18° According to Washburn. 

shown that, over a measurable concentration interval, points on the curve 
necessarily lie upon a horizontal straight line. As this has not been 
done, it is evident that Washburn's conclusions remain in doubt. 

The manner in which the curve for the mass-action function ap- 
proaches the axis depends upon the value of the constant m in the 
general equation. For values of m greater than unity, the curve ap- 
proaches the axis asymptotic to a line parallel to the axis of concen- 
trations; while for values of m less than unity, it approaches the axis 
asymptotic to the axis of K'. In the case of water, therefore, for which 
the value of m appears to be less than unity, we should expect that the 
K' curve would be everywhere concave toward the axis of concentrations. 



100 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

The conductance of potassium chloride solutions between the concen- 
trations of 10-"= and 2 X 10"° normal may be represented well within the 
limits of experimental error, by means of the Equation 11 ^^ in which 
the constants have the value: m = 0.52, D = 1.703, Ap = 129.9, and 
Z = 10 X 10-*. Washburn's value for K is 200 X 10'* Actually, this 
represents an upper probable limit for the value of the constant K. 
The value 10 X 10"* would appear to be too small. Salts in the alcohols 
have values of the mass-action constant considerably greater than this. 
Since, in general, the value of the mass-action constant increases with 
the dielectric constant, we should expect that the value of this constant 
in the case of aqueous solutions would be greater than in the alcohols. 
It should be noted, however, that the experimental results might still 
be represented within the limits of experimental error if a value con^ 
siderably greater than 10 X 10"* were assumed for the mass-action con- 
stant. It is possible, therefore, that the salts in water may have a value 
of the mass-action constant as high as 100 X 10"*. On the other hand, 
so far as the actual data are concerned, it cannot be definitely demon- 
strated that the mass-action law is approached as a limiting form in 
aqueous solutions of strong electrolytes. Even the value of 200 X 10"* 
for potassium chloride appears to be distinctly lower than the value of 
the constants for certain much weaker electrolytes in aqueous solution, 
as, for example, acids of intermediate strength. 

In the case of the strong acids and bases, sufficient data are not 
available to determine the order of magnitude of the limit which the 
function K' approaches. If the data relating to hydrochloric acid are 
correct, the ionization of this acid in a 10"* normal solution is as low 
as that of potassium chloride at the same concentration, assuming that 
the value of Ao for hydrochloric acid is 380.0. Actually this value of 
A„ is somewhat too low and the value 382.0 is probably more nearly 
correct. It would appear, therefore, that the strong acids may approach 
a value of the mass-action constant as low or lower than that of the 
salts; or, in other words, values lower than 200 X 10"*. No data are 
available from which the ionization of the strong bases may be calculated 
at low concentrations. 

The limiting values which the ionization constants of the strong acids 
and bases approach at low concentrations is of considerable practical 
importance, since the hydrolysis of salts depends upon the relative values 
of these constants and that of water. If the values which the mass- 
action constants of the bases and acids approach at low concentrations 
are sufficiently small, then the salts of these acids and bases will be 

" Kiaus, loc. cit. 



FORM OF THE CONDUCTANCE FUNCTION 101 

hydrolyzed to an appreciable extent at very low concentrations. In 
case the limits approached differ for the acids and the bases, the meas- 
urement of the conductance of very dilute salt solutions will be affected 
by hydrolysis. It appears not impossible that the bases may approach 
values of the mass-action constant lower than those of the acids. In 
liquid ammonia solutions the ionization constants of the bases are much 
lower than those of the acids. We might, therefore, expect that at con- 
centrations approaching 10"'^ normal the conductivity of the salt might 
be appreciably affected by hydrolysis. This is almost certainly the case 
with silver nitrate. The ionization constant of this base is approxi- 
mately 2.5 X 10"* at 25°. This value is based on the solubility of a 
saturated solution of silver oxide in water whose ionization has been 
determined to be approximately 0.64. At 10"^ normal the conductance 
of the silver nitrate solution would be affected to the extent of 0.7 per 
cent due to hydrolysis. Until more accurate data are available on the 
ionization of the strong acids and bases at low concentrations, the inter- 
pretation of conductance measurements with salts at low concentrations 
remains in doubt. 

5. Solutions of Formates in Formic Acid. It is evident, from the 
considerations of the foregoing sections, that, as the concentration of an 
electrolyte increases, the value of the function K' increases. In other 
words, as the concentration of the electrolyte increases, the conductance 
falls less rapidly than required by the simple mass-action relation. As 
we have seen, if the simple mass-action law holds, then a plot of the 
reciprocal of the equivalent conductance against the specific conductance, 
or the ion concentration, yields a linear relation between the experi- 
mentally determined points. Deviations from the mass-action law are 
then, obviously, such that at high concentrations the points diverge from 
a straight line toward the axis of specific conductances. In general, 
therefore these curves are concave toward the axis of specific con- 
ductances. There are indeed a few cases in which the curves are convex 
toward the axis of specific conductances, or, in other words, in which 
the deviations from the mass-action relation are in the opposite direction. 
This has been found to be the case with aqueous solutions of certain 
weak organic acids whose viscosity is very high. Presumably this form 
of the curve is due to the rapidly increasing viscosity of the solution at 
higher concentration. The same form of curve has been found by 
Schlesinger and his associates for solutions of formates in formic acid.^* 



« c!„i,io=fnP-pr and Calvert, J. Am. Chem. Soc. SS, 1924 (1911) ; Schlesinger and 

" S<=?l':f™%em Soc gfi! 1589 (1914) ; Schlesinger and Coleman, J. Am. Chem. Soc. S8. 

^,^/*J?bi'fil • SchlesTnge? and MuUtalx, J. Am. Chem. Soc. H, 72 (1919) ; Schlesinger and 

R d J Am Chem Soc. k 1921 (1919) ; Schlesinger and Bunting, J. Am. Chem. Soc. V. 



102 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

According to Schlesinger, solutions of the formates in formic acid 
present an anomaly in that, while they are highly ionized, differing but 
little in this respect from aqueous solutions, the simple law of mass-action 
is obeyed up to concentrations as high as 0.3 normal. If this interpreta- 
tion is correct, it will be necessary to revise all commonly accepted notions 
relative to the causes underlying the deviations from the simple mass- 
action law, since in these solutions we would have a case in which the 
law of mass-action is obeyed up to high concentration for solutions of 
strong electrolytes. We may, therefore, examine the results obtained 

Specific Conductance of Sodium Acetate in Water. 

)0. 20. 30. 40. SO 60. 70 



.029 
.027 

.025 
U 
Is .023 

e 

3 .021 

3 

-3 .017 

o 
02 

, .015 

.013 
.Oil 



f 


y^ 


/ o> 




c{ 


^^^""^ / 


n 


-X**^ y< ^^ 




^^^-""^ 




«=*^^I.O 




_y^'0.l 


• 



.036 
.03+ 

.osa 

.030 

.ose 
.oze 

.024' 
.022 
.020 

.oie 

. 016 
.014. 



a 

3 

•■a 

o 

GQ 



0. 5. iO. 15. Za 25. 30. 35. 

Specific Conductance of Sodium Formate in Formic Acid. 
Fig. 15. Comparison of Conductance Curves in Formic Acid and in Water. 



in formic acid with some care in order to determine whether or not solu- 
tions in this solvent may be brought into line with solutions in other 
solvents. 

It is at once apparent that measurements with solutions in formic 
acid may lead to difi&culties of interpretation, owing to the fact that the 
conductance of the pure solvent is very high. It is not possible to 
carry the measurements to very low concentrations ; and if such measure- 
ments are carried out, the results will always be more or less in doubt. 
In Figure 15, the upper curve represents a plot of 1/A against the 
specific conductance for solutions of sodium formate in formic acid, 
according to Schlesinger. It will be observed that, between a concen- 
tration of C = 0.0667 and C = 0.297, the points lie upon a straight line 
within the limits of experimental error. At lower concentrations the 
curve deviates from a straight line, being concave toward the axis of 



FORM OF THE CONDUCTANCE FUNCTION 103 

ion concentrations, wliile at iiigiier concentrations it is convex toward 
this axis; in other words, the experimentally determined points lie upon 
a curve which has an inflection point somewhere between the concentra- 
tions given above, probably in the neighborhood of 0.1 normal. Schles- 
inger is inclined to attribute the deviation of the points in the more 
dilute solutions to the presence of impurities. So far as the conductance 
of the solvent is concerned, since sodium formate has an ion in common 
with formic acid, it is to be expected that the ionization of formic acid 
itself will be repressed by sodium formate, so that the conductance of the 
pure solvent itself will not enter. He believes, however, that there are 
present in the solvent impurities, as a result of which the measured con- 
ductance is higher than that due to the electrolyte. On the other hand, 
it is known that the salts of the fatty acids yield ions which move very 
slowly and whose solutions exhibit an extremely high viscosity. The 
form of the curve in the case of the formates in formic acid is similar 
to that of certain acids in water. Further light may be thrown upon 
this question by considering the conductance curves of salts of organic 
acids in water, whose solutions likewise exhibit a high viscosity. The 
lower curve in Figure 15 represents a plot of 1/A against the specific 
conductances for sodium acetate in water at 18°. An inspection of the 
figure shows at once that the curve for sodium acetate in water is in all 
respects similar to that of sodium formate in formic acid. Between the 
concentrations 0.1 and 0.5 normal, the points lie upon a straight line 
within the limits of experimental error. In the more dilute solutions, 
the experimentally determined points lie upon a curve concave toward 
the axis of concentrations and in the more concentrated solutions on a 
curve convex toward this axis. In the case of sodium formate in formic 
acid, the concentration interval over which the points lie upon a straight 
line is 0.0667 to 0.297, corresponding to a concentration ratio of 4.45, 
while in the case of sodium acetate in water the corresponding concen- 
tration interval is 0.1 normal to 0.5 normal, whose ratio is 5.0. If we 
hold that the law of mass-action applies to solutions of sodium formate 
in formic acid, we might equally well hold that this law applies to solu- 
tions of potassium acetate in water. Our knowledge of the behavior of 
aqueous solutions, however, is such that it is at once evident that the 
linear form of the curve between 0.1 and 0.5 normal is due to the fact 
that, owing to the high viscosity of the solutions at higher concentra- 
tions, the conductance as measured is smaller than it otherwise would be. 
On the other hand, in the more dilute solutions the form of the curve 
in the case of sodium acetate is entirely similar to that of other 
binary electrolytes in water. It is difficult, therefore, to escape the con- 



104 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

elusion that in the case of solutions of the formates in formic acid, 
likewise, the approximately linear form of the curve over a limited con- 
centration interval is due to the existence of an inflection point and that 
the causes underlying the course of the curve are the same as those in 
solutions of sodium acetate in water. It appears probable, therefore, 
that solutions of the formates in formic acid do not constitute an excep- 
tion to the well-known behavior of strong electrolytes in solvents of high 
dielectric constant. From this point of view these solutions are normal 
in their behavior. 

6. The Behavior of Salts of Higher Type. Up to this point, the 
electrolytes considered have been of the binary type. In the case of 
salts of higher type the interpretation of conductance measurements 
becomes much more difficult and uncertain, since it is possible, and even 
probable, that ionization may take place in several stages, as indeed it 
does in the case of weak acids and bases. For example, a salt of the 
type MXj may ionize according to the equations: 

MX^ = MX^ -1- X- 
MX* = M+* + X- 
MX;, = M** + 2X-. 

If ionization takes place only according to the last equation, then the 
degree of ionization may be calculated from conductance measurements. 
But if ionization takes place according to the first two equations, then it 
is not possible to determine the number of carriers in the solution at a 
given concentration. In the case of weak dibasic acids, ionization often 
takes place according to the first two equations, the constants of the 
two reactions being such that one reaction is practically completed before 
the other reaction has begun. With salts this does not appear to be 
the case. 

In any case, if the concentration is sufficiently low, we should expect 
that, ultimately, there would be present in the solution only the ions M** 
and X-. Since the ion M** carries two charges, its carrying capacity 
will be approximately twice as great as that of an ion carrying only a 
single charge. The molecular conductance of such an electrolyte should 
therefore approach a value approximately twice that of a binary electro- 
lyte, or its equivalent conductance should approach a value of the same 
order as that of binary electrolytes. An examination of the conductances 
given in Table III indicates that this is the case. The limiting value 
of the equivalent conductance for salts of different type is throughout 
of the same order, and we may conclude, therefore, that at low concen- 



FORM OF THE CONDUCTANCE FUNCTION 105 

trations the carrying capacity of an electrolyte is determined by the 
number of charges associated with the ionic constituents. 

In solutions of salts of the type of copper sulphate, reaction may take 
place according to the equation: 

CuSO^ = Cu^^ + SO,-. 

This reaction is a binary one, similar to that of the binary salts, but 
the molecular conductance of such a salt should be twice that of a binary 
salt. Such has been found to be the case. 

This behavior of salts of higher type appears to be quite general 
and is not confined to aqueous solutions. In Table XXXIV are given 
conductance values for solutions of strontium and barium nitrates in 
ammonia. It will be observed that in both cases the limiting value of 
the molecular conductance is much higher than that of binary electro- 
lytes and is, in fact, approximately twice that of these electrolytes. We 
may assume, therefore, that in these solutions we have ultimately a 
reaction corresponding to the type: 

Sr(N03)2 = Sr+^ + 2N03-. 

It is apparent, however, that at a given concentration the number of 
carriers present in solutions of these electrolytes is much lower than it is 
in solutions of typical binary electrolytes. Owing to the low value of 
the ionization, the values of Ao for electrolytes of this type have not been 
determined with any degree of certainty. 

TABLE XXXIV. 

Conductance of Teenary Salts in NH3 at — 33°. 

Sr(N03),^^ Ba(N03),'=« 

V Amol y ■'^mol 

286.2 145.0 91.1 101.3 

1283.0 207.0 1407.0 200.6 

54410 275.8 14950.0 319.4 

20360.0 359.3 58750.0 422.5 

61660.0 449.0 116500.0 498.5 

151100.0 514.2 

Similar results have been obtained with solutions of ternary electro- 
lytes in various other solvents, such as acetone, pyridine, and the like. 
In many cases, however, the solubility of these salts is relatively low 
and their ionization at ordinary concentrations is often extremely small. 
They do not, therefore, lend themselves to a quantitative study of the 

M Franklin and Kraus, Am. Chem. J. 2S, 292 (1900) 
s»E^aSklln and Kraus, J. Am. Chem. Soc. 27. 200 (1905). 



106 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

relation between the conductance and the concentration. In the case 
of aqueous solutions, however, sufficient data are available to make it 
possible to obtain a general notion as to the manner in which the con- 
ductance varies as a function of concentration. Assuming a reaction of 
the type 

MX^ = M*^ + 2X-, 

and assuming the mass- action law to apply, we obtain the equation: 

1 — Y 

In Table XXXV are given values of the function K' calculated 
according to the above equation at a series of concentrations for calcium 
chloride dissolved in water at 18°. 







TABLE XXXV. 






Values of the 


Mass-Action Function 

IN H^O AT 18°. 


FOB CaClz Solution 


c . 


, . . . 10-" 
.954 
.v.." 1.88X10-' 


5X10-' 2X10-" 

.910 .849 

1.7X10-' 1.62X10-' 


10-1 5X10-1 
.764 .686 
1.88X10-' 2.6X10-' 



It will be observed that the mass-action function for this salt increases 
very greatly with the concentration. On the whole, the increase is much 
more marked than it is for binary electrolytes. The value of the func- 
tion, moreover, is much lower throughout than it is for solutions of binary 
electrolytes. At 5 X 10"i normal the value of K' is only 0.26, which is 
approximately one-half that of potassium chloride, while at 10"^ normal 
the value is 1.88 X 10"°- The mass-action function, therefore, falls off 
very rapidly as the concentration decreases. In the case of copper sul- 
phate solutions we have the equation: 

1 — Y 

Values of the mass-action function for this electrolyte at different con- 
centrations are given in Table XXXVI. At higher concentrations the 
value of the function K' for this salt is smaller than that for calcium 
chloride, but the constant decreases much less rapidly as the concentra- 
tion decreases and at lower concentration the value of the function is 
much greater than that of calcium chloride. On the whole, the function 
appears to undergo a smaller change with the concentration in the case of 
copper sulphate than in that of uni-univalent electrolytes. However it 



FORM OF THE CONDUCTANCE FUNCTION 107 

is to be borne in mind that the value of Ao for this electrolyte is much 
less certain than that for the uni-univalent salts. 

TABLE XXXVI. 

Value op the Mass-Action Function fob CuSO^ in H^O at 18°. 

C 10-^ 5X10-« 2X10-^ 10-1 10 

Y%---- 86.2 70.9 55.0 39.6 30 9 

K 5.4X10-^ 8.6X10' 1.34X10-2 2.6X10"' 1.38X10-' 

As the salts become more complex, the value of the mass-action func- 
tion becomes smaller and decreases more rapidly as the concentration 
decreases. For potassium ferrocyanide, assuming the reaction equation: 

K^FeCNe = 4K* + FeCNe-", 

the mass-action function has the form: 

JCyy _^, 
C(l-Y)~ 

Values of the function at different concentrations are given in Table 
XXXVII for this salt, as well as for lanthanum sulphate. The constant 
for the ferrocyanide is throughout small and at low concentrations 
approaches values of an entirely different order of magnitude from that 
at the higher concentrations. In the case of lanthanum sulphate, the 
change in the constant is even more pronounced, as may be seen from 
an inspection of the table. 

TABLE XXXVII. 

Values of the Mass-Action Function of Aqueous Salt Solutions. 

K^FeCNe 

C 2X10-' 1.25X10-2 5.0X10"' 1.0X10-' 3.0X10-^ 4.0X10"^ 
Y% 85.8 71.0 68.7 53.2 48.8 45.3 

K .52X10" 1.5X10-' 1.03X10-' 0.920X10-' 4.33X10"* 0.925X10-' 

La^CSOJa 

C 2X10-' 10"2 5X10-' 

Y% 51.4 33.9 26.2 

K 1.28X10-1' 0.67X10-" 1.03X10-' 

It is obvious that, in solutions of electrolytes of higher type, the 
mass-action function varies the more the higher the type of the salt. 
The value which the function appears to approach at very low concen- 



108 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

trations becomes extremely small and it is uncertain whether or not the 
function approaches a limiting value other than zero. The interpreta- 
tion of the results, moreover, is rendered uncertain owing to the possible 
formation of intermediate ions. It might be expected, however, that, 
in the limit, the intermediate ions will disappear and the function will 
correspond to the usual mass-action function. 

Although the curves become quite complex for salts of higher type, 
it appears, nevertheless, that the conductance curves at higher concen- 
trations have the same general form as for salts of simpler type, and that 
they vary in a similar manner as the nature of the solvent varies. In 
the following tables are given values for the conductances of Cu(N03)2 
and KjHgCCN)^ in ammonia." 

TABLE XXXVIII. 
Conductance of Teenahy Salts in NH. at — 33°. 



Cu(N03), 


K. 


Hg(CN), 


V 


A 


V 


A 


1.5 


98.3 


2.0 


198.8 


4.9 


82.9 


5.0 


182.7 


9.9 


78.2 


19.6 


159.8 


19.9 


80.9 


49.8 


169.2 


323.0 


151.8 


590.0 


298.9 


1300.0 


213.7 


4545.0 


493.1 


11190.0 


417.0 






22450.0 


498.0 







It will be observed that, in both cases, the conductance passes through 
a minimum value at concentrations in the neighborhood of 0.1 normal. 
In other words, an increase in the conductance with the concentration at 
the higher concentrations is not confined to binary electrolytes, but is 
more or less typical of all electrolytes. It appears, therefore, that the 
general form of the conductance function is the same for electrolytes of 
different types. What the precise form of the equation may be, however, 
has not been determined, since the A„ values are unknown and the prob- 
lem is complicated owing to the possible formation of intermediate ions. 

"J Franklin, Ztschr. f. phys. Ohem. 69, 272 (1909). 



Chapter V- 

The Conductance of Solutions as a Function of 
Their Viscosities. 

1. Relation Between the Limiting Conductance Aq and the Viscosity 
of the Solvent. One of the factors upon which the conductance of a 
solution depends is the viscosity of the solution itself. If conductance 
is due to the motion of charged particles through a medium, then the 
speed of the particles will obviously depend upon the resistance which 
the particles experience in their motion; that is, upon the viscosity of 
the medium. Unless the solutions are concentrated, their viscosities will 
not differ materially from that of the pure solvent. We should therefore 
expect that the viscosity of the pure solvent would determine the motion 
of particles under otherwise given conditions. We shall accordingly 
examine the relation between the conductance and the viscosity of solu- 
tions in different solvents. In very dilute solutions we may expect that 
the motion of a given particle will be practically independent of that of 
other particles of the electrolyte which may be present in the solution. In 
the limit, therefore, the Ao values will be determined by the nature of the 
moving particles and by that of the solvent medium in which they move. 
In Table XXXIX ^ are given fluidity and Ao values for solutions in a 
number of solvents, together with the values of the ratio Ao/F. 

TABLE XXXIX. 

Fluidity and Ao Values for Electrolytes in Different Solvents. 

Solvent Temp. F = l/cp Ao Ao/F Electrolyte 

Water 18° 93.9 111.0 1.173 Nal 

Ammonia —33° 391.0 301.2 0.770 " 

Sulphur dioxide — 10° 233.4 199.0 0.854 KI 

Benzonitrile 25° 80.0 49.0 0.613 Nal 

Epichlorohydrin 25° 97.1 62.1 0.649 (C2H,),NI 

Propylalcohol 18° 42.5 20.6 0.486 Nal 

Acetone 18° 304.0 167.0 0.550 

Methylethylketone 25° 249.0 139.0 0.560 " 

Pyridine 18° 101.0 61.0 0.603 " 

Isobutylalcohol 25° 29.6 13.7 0.463 " 

Acetoaceticester 18° 59.4 30.7 0.517 " 

Isoamylalcohol 25° 27.2 9.2 0.338 

Ethylenechloride 25° 127.9 66.7 0.522 (C3H,),NI 

"These values are taken from Kraus and Bray (.loc. cit., p. 1383), excepting those tor 
water and the viscosity data for sulphur dioxide for which see Fitzgerald, J. Phya. Chem. 
16, 621 (1912). 

109 



no PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

So far as possible the same electrolyte, namely sodium iodide, has been 
employed for the purpose of comparison. In a few cases, however, 
results with this electrolyte are not available and the data for other 
iodides are therefore given. If the speed of the ions is solely a function 
of the viscosity of the solvent and is independent of the nature of the 
electrolyte, the nature of the solute will have no influence on the ratio of 
conductance to fluidity. As we shall see below, this is not the case.^ 
On examining the table it will be seen that the limiting value of the 
conductance is roughly proportional to the fluidity of the solvent. The 
ratios A„/F given in the last column vary between 0.338 for isoamyl- 
•alcohol and 1.173 for water. These are, however, extreme values, and in 
the greater number of cases the ratio has a value of approximately 0.6. 
The three inorganic solvents, water, ammonia and sulphur dioxide, show 
exceptionally high values of the conductance-fluidity ratio. The 
higher alcohols have exceptionally low values, the value in general 
being the smaller the more complex the alcohol. In comparing 
the Ao values of the salts in different solvents, we are comparing the 
sum of the conductances of the two ions. We may therefore expect 
to obtain a more nearly comparable result if we compare the con- 
ductances, not of the electrolytes, but of the individual ions of the elec- 
trolytes. The ratios of the ionic conductances for the different ions in 
ammonia and in water have been given in Table V. An examination of 
that table shows that the ratios of the ionic conductances vary all the 
way from 2.03 to 3.36, while the ratio of the fluidities of the two solvents 
is 4.15. It follows, therefore, that the ratio of the Aq values for a given 
electrolyte in different solvents cannot be a constant, since the ratios of 
the ion conductances vary for different ions. 

If a comparison is to be made between the conductance and the 
fluidity of electrolytes in different solvents, it might be expected that 
more nearly comparable results would be obtained if the more slowly 
moving ions were chosen for the purpose of comparison. For example, 
in water at 18°, the ratio of the conductance of the acetate ion to the 
fluidity of water is 0.367,^ while in ammonia the ratio of the conductance 
of the CH3CONH- ion to the fluidity of ammonia at its boiling point 
is 0.330. 

Apparently, therefore, the ratio of the ionic conductance to the 
fluidity of the solvent approaches a constant limiting value somewhere 

» Walden [Ztschr. f. phys. Chem. 78, 257 (1912)] believes to have shown that, with a 
few exceptions, the rntio A^/i? is constant. In this he has been misled as a result of 
employing Ao values obtained by extrapolating with the cube root formula of Kohlrausdi 
whicli is not applicable. 

'' Based on tlie value 34.6 for the conductance of the acetate Ion. Johnston, •/. ^m. 
Ohem. *'9C. St, 1010 (1909). 



THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES HI 

in the neighborhood of 0.3 as the ions become more complex; that is, 
as the speed of the ions decreases. It follows that, in the case of very 
slowly moving ions, the speed is inversely proportional to the viscosity 
of the medium, more or less independent of the nature of the solvent 
itself. It is interesting to compare the speed of ions due to radiations 
with the speed of ordinary ions in different solvents. In Table XL* 
are compared the speeds of the acetate ion in water, the lithium ion in 
ammonia, and the positive and negative ions in hexane. In the last 
column are given the values of the ratio of the speed of the ions to the 
fluidity in arbitrary units. 

TABLE XL. 

COMPAEISON OF lONIC SpEEDS IN DIFFERENT SOLVENTS. 

Speed of ion 
Solvent Ion S X 10* F S/F 

Water Acetate 3.58 95.35 3.76 

Ammonia Lithium 11.60 390.8 2.97 

Hexane Positive 6.03 312.0 1.98 

Hexane Negative 4.17 312.0 1.34 

It will be observed that both positive and negative ions in hexane move 
decidedly slower than even the slowest moving ion in ammonia or in 
water, taking into account the relative viscosities of the solvent media. 
Apparently, in solvents of very low dielectric constant, the speed of the 
ions relative to the fluidity of the solvent is smaller than it is in solvents 
of higher dielectric constant. It may be inferred, therefore, that the 
positive and negative carriers in hexane are associated with a con- 
siderable number of the solvent molecules, as a result of which their 
speed is relatively low with respect to that of the ordinary ions in water 
and ammonia. 

2. Change of Conductance as Result of Viscosity Change Due to the 
Electrolyte Itself. At higher concentrations the viscosity is a function 
of the concentration of the solution, and, in most cases, increases with 
it. In aqueous solutions there are, however, many eases in which the 
viscosity decreases at higher concentrations, or rather, in which the vis- 
cosity passes through a minimum, beyond which it again increases as the 
concentration increases. The viscosity effect of the electrolyte, there- 
fore, is a property depending on the electrolyte as well as on the solvent. 
Solutions which exhibit a negative viscosity change with the concentra- 
tion, that is, whose viscosity decreases with increasing concentration, are 

*Krms, f. Am. Ohem- Sqo. S6, §5 (J3J4), 



112 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

also found in glycerine. In general, however, the negative viscosity 
effect appears only in the case of solutions in solvents having high dielec- 
tric constants. As a rule, only those salts which show relatively a slight 
tendency to form stable hydrates exhibit a negative viscosity effect in 
solution. In Table XLI are given examples of the relative viscosities of 
solutions in ammonia,^ water, and methylamine " at a number of con- 
centrations. 

TABLE XLI. 

COMPAEISON OF THE ViSCOSITY ChANGE DuE TO ELECTROLYTES IN 

Different Solvents. 

Solvent ■ Solute Relative Viscosity at Concentration: 

0.5 1.0 2.5 



Water 


.. LiCl 


1.05 


1.10 


1.42 


Ammonia 


.. KI 


1.16 


1.38 


2.38 


Methylamine . . 


.. AgN03 


1.40 


1.96 


6.38 



It will be observed that in a 0.5 normal solution the viscosity increase 
for potassium iodide in ammonia is approximately three times that of 
lithium chloride dissolved in water, while the viscosity change for silver 
nitrate in methylamine at the same concentration is approximately three 
times that of potassium iodide in ammonia. Approximately the same 
ratio of increase holds at somewhat higher concentrations. In this con- 
nection it should be noted that the viscosity effect in the case of lithium 
chloride is relatively very great compared with that of other salts in 
water. In the case of potassium iodide the viscosity effect is actually 
negative in water. We see, therefore, that the lower the dielectric con- 
stant of the solvent, the greater is the increase in viscosity due to the 
added electrolyte. The dielectric constants are approximately 80, 22 
and 10 for water, ammonia, and methylamine respectively. There are 
no data available relative to the viscosity of solutions in the higher 
amines, but qualitative data indicate that the viscosity effect increases 
very greatly with increasing complexity of the solvent, or, rather, with 
decreasing dielectric constant of the solvent. It is evident that there is 
a relation between the magnitude of the viscosity effect due to an elec- 
trolyte and the dielectric constant of the solvent in which this electrolyte 
is dissolved. 

In Figure 16 are shown curves' representing the relation be- 
tween the viscosity and the concentration of aqueous solutions of 

° Fitzgerald, loc. cit. 

•Sprung, Pogg. Ann. d. Phya. 159, 1 (1876). 



THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 



113 



potassium iodide at 0°, 30°, and 60° and sodium chloride at 10°, 30°, and 
60°. It will be observed that the viscosity in the case of potassium 
iodide at 0° passes through a minimum in the neighborhood of 2y2 nor- 
mal, after which it again increases. At higher temperatures the minimum 
is displaced toward lower concentrations and finally disappears. The 
negative viscosity effect decreases rapidly with increasing temperature 
and in most cases disappears in the neighborhood of 30°. At still higher 
temperatures the viscosity effect becomes positive. In general, the posi- 
tive viscosity effect increases markedly with the temperature. 




0,0 1.0 2.0 3.0 4.0 S.O 

Concentration. 
Fig. 16. Viscosity of Aqueous Solutions at Different Concentrations. 



In glycerine solutions,' ammonium iodide, potassium iodide, and 
rubidium iodide exhibit negative viscosity effects. Lithium chloride, on 
the other hand, as in water, exhibits a viscosity increase with increasing 
concentration. In glycerine solutions, the negative viscosity effect dis- 
appears in the neighborhood of 75°. 

It is obvious that, if the viscosity of a solution changes with concen- 
tration, the speed of the carriers, to which the conductance of the solu- 
tions is due, will likewise change with the concentration. If this is the 

case, then the conductance ratio, y = t", no longer measures correctly 

'Davis and Jones, Ztschr. f. phys. Chem. 81, 68 (1913), 



114 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the degree of ionization. It has been proposed to take account of the 
change of conductance due to the viscosity effect in direct proportion to 
the fluidity change of the solution.^ In that case the degree of ionization 
of the electrolyte is given by the expression: 

(40) V = t§, 

where F^ is the fluidity of the pure solvent and F that of the solution. 
Other writers ° have proposed an equation of the form: 



(41) Y 



~Ao\Fj ' 



where p is a constant, and A and Ao are ionic conductances. If p were 
equal to unity, the conductance of the solution would be corrected in 
direct proportion to the fluidity change. Difiiculty arises in determining 
the value of p. It has been suggested that the value of this constant 
may be derived from the manner in which the speed of an ion in dilute 
solution changes as a function of the temperature. As we shall see 
presently, the change in the Ao values of the ions is not in general 
directly proportional to the fluidity change of the solvent, but is in most 
cases smaller. It has been shown that a relation of the type 

(42) A = KFP 

holds very nearly." The values of the constant p for different salts are 
given in Table XLII. 

TABLE XLII. 

Value of the Viscosity-Tempebatcee Exponent p fob 
Different Ions. 

Univalent Ions. 

Ion CI- K* NH,* NO3- Ag^ Na* CH3COO- 

P 88 .887 .891 .807 .949 .97 1.008 

A 65.4 64.7 64.4 61.8 54. 43.5 34.6 

Divalent Ions. 

Ion 1/2 SO,- 1/2 C A" 1/2 Ba** 1/2 Ca** 

P 0.944 .931 .986 1.008 

A 68.7 63.8 55.9 52.1 

• Washburn, J. Am. Chem. 8oc. SS, 1463 (1911). 
"Johnston, J. Am. Chem. Soo. SI, 1010 (1909). 



THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 115 

Since p is in general less than unity, it follows that the conductance of 
the ions changes less rapidly than does the viscosity of the solvent for a 
given increase in temperature. As a rule, the lower the conductance of 
the ion, the greater the value of the exponent p. For most slowly mov- 
ing ions the exponent appears to approach the value unity as a limit. 
This is exemplified in the case of the acetate and the calcium ions. The 
lower the conductance of an ion, therefore, the more nearly does the 
conductance change in direct proportion to the fluidity change of the 
solvent. But while the value of p in Equation 42 has thus been evalu- 
ated, there is no good reason for believing that the exponent p in Equa- 
tion 41 will have the same value. It obviously is not possible to deter- 
mine the manner in which correction should be applied for the change 
in the conductance of solutions due to concentration change, unless we 
know the manner in which the ionization at these concentrations varies 
as a function of concentration. In other words, the nature of the cor- 
rection as found will depend upon the assumed nature of the conductance 
function. 

We have the equation: 

-^t-^K' = f(C), 



where /(C) is some function of the concentration of the solution. As we 
have seen, in solutions at higher concentrations, the function K' follows 
approximately the relation: 

(9-) Cll^ = ^' 

where n has a value' in the neighborhood of 1.5 for aqueous solutions. 
Assuming this equation to hold at higher concentrations, we may deter- 
mine the nature of the viscosity correction on the basis of this assump- 
tion. In order to determine the nature of the correction, therefore, we 
may determine the value of the constants n and D at lower concentra- 
tions, whA'e the viscosity change is negligible, and thereafter extrapolate 
this function to higher concentrations. In other words, by means of 
Equation 9a we may calculate the value of y at higher concentrations 
and compare it with the directly measured value and with the fluidity 
of the solution at that concentration. Or, conversely, the experimentally 
determined conductance values at higher concentrations may be multi- 
plied by an assumed correction factor and the corrected values compared 
with the values calculated by means of the above equation. If the 
assumptions made are applicable, then the two values should correspond. 



116 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

The simplest correction would be that in which the conductances were 
assumed to change in direct proportion to the fluidity change of the 
solution. 

This method of correction has been applied to solutions of potassium 
iodide dissolved in water at 0°." In Figure 17, lower curve, are plotted 
values of log (CA) and of log[C(A<, — A)], both for the measured (rep- 
Log (cA) for LiCl. 



P 



4 



o 

Hi 













^y 


^ 

* 














^ 


+ 


B 














X 




X 








y 


^ 






A 








^ 








y- 


' + * 












/ 


y 














/ 


y 
















/' 

















bO 

o 



Log (cA) for KI. 

Fia. 17. Showing Influence of Viscosity Correction on the Conductance Curves of 
KI and LiCl in Water at 0°. 



resented by crosses) and the corrected (represented by circles) con- 
ductance values of potassium iodide dissolved in water at 0°. . If Equa- 
tion 9a holds and if the assumed viscosity correction is applicable, then 
the corrected points should lie upon a straight line.^^ This, apparently, 
is the case. 

The conductance curve of potassium iodide in water at 0° is a very 
exceptional one in that at higher concentrations it passes through a slight 
minimum and maximum, after which the conductance decreases very 
rapidly with increasing concentration. This form of the curve is due 

"Kraus, J. Am. Ohem. Soc. 36, 35 (1914). 

"Equation 9a may be written: n log (OA) = log tO'(Ao — A)] + log DAo" 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 117 

to the viscosity change of the solution at higher concentrations. As we 
have seen, the fluidity passes through a maximum, after which it de- 
creases sharply. If the values of the conductance as calculated from 
Equation 9a are multiplied by the fluidity ratio {-, then these calculated 

To 



values fall upon a curve (B) exhibiting a slight m°aximum and minimum, 




ElG. 



ItOg (ConcentrfltioD). 

18. Showing the Influence of Fluidity Change on the Conductance Curve of 
KI in Water at 0°. 



which practically coincides with the curve of measured conductances, as 
may be seen from Figure 18. It is apparent that in the case of solu- 
tions of potassium iodide in water — and, in fact, this has been shown 
to be true for aqueous solutions of all electrolytes exhibiting a negative 
viscosity effect — the speed of the ions changes in direct proportion to the 
fluidity change of the solution. The peculiar form of the conductance 
curve, as we have it in solutions of the potassium iodide, is due to the 
variation of the viscosity effect. 



118 , PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In solutions of electrolytes in water which exhibit a positive viscosity- 
effect, the conductance appears to change less than the viscosity of the 
solution. If we treat the conductance curve of lithium chloride in a 
manner similar to that employed in the case of potassium iodide, we 
obtain as plot not a straight line, but a curve lying below the straight 
line resulting from Equation 9a. In other words, the conductance values 
appear to be overcorrected. This result is illustrated in Figure 17, upper 
curve, in which A is the uncorrected curve, B is the curve in which the 
conductance is corrected in direct proportion to the fluidity change, 
while C is a curve in which correction has been applied to the lithium 
ion only. We may conclude, therefore, that, in aqueous solutions, the 
conductance may be corrected for the viscosity change in direct propor- 
tion to the fluidity change in the case of salts which exhibit a negative 
viscosity effect, but that, in solutions of salts which exhibit a positive 
viscosity effect, the correction made should be smaller. Just what cor- 
rections should be applied is difficult to determine at the present time. 

We have seen that in non-aqueous solutions the viscosity effect is 
much larger than it is in aqueous solutions. We should therefore expect 
that the conductance of non-aqueous solutions would be affected to a 
much greater extent than that of aqueous solutions. It appears, how- 
ever, that in solutions of electrolytes in non-aqueous solvents the con- 
ductance changes much less than the fluidity of the solvent. 

The relation between the conductance and the viscosity is illustrated 
in Figure 19, in which are plotted the conductance and fluidity values 
of solutions of potassium iodide in liquid ammonia at different concen- 
trations. Branch B is extrapolated on the assumption that Equation 9a 
holds. There is also indicated on this figure the calculated conductance 
of these solutions. Branch D, on the assumption that the conductance 
changes in direct proportion to the fluidity of the solvent. It will be 
observed that the condiictance, as corrected in this way, is much too low 
to correspond with the experimental conductance curve represented by 
circles. It is evident, therefore, that in non-aqueous solutions the con- 
ductance change is smaller than corresponds to the viscosity change. 
This is further borne out by the fact that Equation 11 appears to hold 
for solutions of many electrolytes up to concentrations at times as high 
as 2 normal. It is obvious that the viscosity of the solutions at these 
concentrations must be much greater than that of the pure solvent, and 
consequently it follows that the correction to be applied for the viscosity 
change is probably the smaller the greater the viscosity change; that is, 
the lower the dielectric constant of the solvent. On the other hand it 
has been found, in the case of all solutions in non-aqueous solvents that 



THE CONDUCTANCE OF SOLUTION&-VISCOSITIES 



119 



at sufficiently high concentrations, the conductance curve ultimately falls, 
and falls the more rapidly the higher the concentration. There appears 
to be no exception to this behavior. There can be little question but 
that the final decrease in the conductance is due to a large increase in the 
viscosity of the medium. This is illustrated in Figure 20, where the 
conductance of solutions of silver nitrate in methylamine ^^ is repre- 
sented as a function of the concentration. The maximum lies a little 



> 
'B 

a* 



•9* 


^» 


* 
























l6o 




^ 


Nv 




























^ 


^ 






























^ 


\ 


'~~~- 









_ 8 




















X 




"o 


















f 








\ 










«6 














~^ 


\^ 




\d 




O 






















\ 


N 


\ 






«4 








' 












^ 


\^ 


\ 


9 
























^^ 


\\ 


o 


























\ 


^ 































0.9« f^ 



, "2 
0.64 g 

O) 

as 

» -3 



i.a 1.0 0.0 0.8 

L^K (concentration). 

Fig 19 Showing the Influence of Fluidity Change on the Conductance of Solutions 

of KI in NHa at — 33.5 . 

above normal concentration at —33° and is displaced toward higher 
concentrations at higher temperatures. 

3. Relation between Viscosity and Conductance on the Addition of 
Non-Electrolytes. The addition of a non-electrolyte to a solution of an 
electrolyte in most cases increases the viscosity of the solution." The 
conductance change on the addition of a non-electrolyte is in the same 
direction as that of the viscosity change, but in most cases the con- 
ductance change is smaller than the corresponding viscosity change. 

"fn*a^few'^ns?ancis'h^oweter, where the added non-electrolyte forms a stable complex 

i*h V.^ nft^P ions In solution, the addition of a non-electrolyte results in a viscosity 

with one o^^fv^^nie of this effect is found in solutions of certain of the heavy metals 

fn'wftp; w^osf yfscosity te reduced on The addition of ammonia. [Blanchard, J. Am. 

In water whose viscosity u, I e addition of a non-electrolyte causes a 

Ohem 80c. f^„l;il^„o^Jt7 o'njy so long as it combines with the electrolyte to form the 
complex "Beyond thil point tte"visc?sity in general increases with further additlou of 
non-electrolyte. 



120 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



The experimental material available is very incomplete. So far as any 
conclusion may be drawn, however, the conductance change is the more 
nearly proportional to the fluidity change, the smaller the molecules of 



3 

a 
o 
O 



C3 

3 









/ 


45 


■ 




1 

Hi 


40 


. 




!> 




-5* 






35 


/ o" \ 




// / 




/ ^"^^ \ 








\ 




1 




/ ,'° V 




If / 


30 


IIP \ 


\\ 


/// 




1 ' ■ ^ 




// 




i 


\\ 


/// 


25 


1 r . 




\ # 




\ 




ZO 


• // / 


N, 






hi ! 




^^^^^.^^ 




;.'/ 






IS 


■Ill 






to 


1! 1 
Hi 

11 




• 


S 


■ i 








1 







O I z 3 

Log V. 
Fig. 20. Conductance of Silver Nitrate in Methylamine at Different Temperatures. 

the added non-electrolyte. It has been found that the relation between 

the conductance and the viscosity on the addition of a non-electrolyte 

may be expressed by an exponential equation of the form Ao ^ KF^, 

where Ao is the limiting conductance of the electrolyte in solutions con- 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 121 

taining the non-electrolyte and F is the fluidity of the solution. The 
smaller the conductance change of the electrolyte for a given fluidity 
change, the smaller is the value of the exponent p. 

In Table XLIII are given values of the exponent p for aqueous 
solutions of a number of electrolytes in the presence of non-electrolytes. 

TABLE XLIII. 

Change of Conductance of Electrolytes Due to Added 
Non-Electrolytes. 

T^^lw °; . a X .^^^- ^^y- ^«e- Methyl 

Electrolyte Sucrosef finose* cerolf tone $ Ureaf Alcohol* 

Mol. Wt 342.1 594.4 92 58 60 32 

P ioT KCl 0.66 0.675 0.83 0.93 0.95 12 

t 20° 25° 20° 25° 25° 25° 

■NT T., X , , Methyl Methyl 

JNon-EIectrolyte Sucrosef Raffinose* Raffinose* Alcohol* Alcohol* 

Electrolyte HCl CsCl LiCl CsCl LiCl 

P 0.55 0.676 0.669 0.8 1.1 

t 25° 25° 25° 25° 25° 

Non-Electrolyte AcetoneJ Glycerol§ Urea§ Pyridine§ 

Electrolyte HCl CuSO, NaOH LiNO, 

P 1.0 1.0 1.0 1.0-1.3 

t 25° 15° — 25° 

♦Clark, Thesis, UniT. of 111. (1915). See also, Washburn, "Principles of Physical 
Chemistry," 2 Ed., p. 260. • f j 

t, Oholm, Finaha Vetenakap. Soc. Forhandl. 55, A No. 5, p. 75 (1913) ; Washburn, 

t Ryerson, Thesis, Univ. of lU. (1915). 
S Green, J. Ohem. Soc. 93, 2049 (1908). 

It will be seen from the table that, in general, the higher the molecu- 
lar weight of the added non-electrolyte, the smaller is the value of 
the exponent p. This is most clearly shown in the case of potassium 
chloride, for which electrolyte the data are more extensive than for 
others. The exponent in the presence of sucrose and raffinose is in the 
neighborhood of 0.67, while in the presence of urea it is 0.95 and in the 
presence of methyl alcohol 1.2. The molecular weight of the added elec- 
trolyte is thus a governing factor in determining the manner in which 
the conductance of an ion varies due to viscosity change. That some 
transpositions in the order of the exponent and in that of the molecular 
weight of the added non-electrolyte will occur is to be expected, since 
specific influences may make themselves felt. It is noticeable that in 
the case of methyl alcohol the exponent has a value greater than unity. 



122 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

The significance of this result remains uncertain. It is to be expected, 
however, that, on the addition of an electrolyte whose molecular weight 
is lower than the mean of that of the solvent molecules, effects may occur 
which cannot well be predicted on the basis of our present knowledge of 
the viscosity relations in such mixtures. It is interesting to note that, 
in the presence of non-electrolytes of high molecular weight, the coeflS- 
cient for different electrolytes has very nearly the same value. Thus, 
in the presence of rafRnose the values of the exponent for lithium, potas- 
sium and caesium chlorides are very nearly identical. Since these salts 
have a common anion, it may be inferred that the influence of the vis- 
cosity effect due to non-electrolytes of high molecular weight is the same 
for the lithium, potassium and caesium ions. This is apparently not so 
nearly true in the presence of non-electrolytes of low molecular weight, 
but even here, in some instances at any rate, the exponent does not differ 
greatly for different salts. It would seem that the influence of the vis- 
cosity change on the conductance of an ion, due to the electrolyte itself, 
differs markedly from that due to the addition of a non-electrolyte. At 
the present time, sufficient data are not available to enable us to draw 
conclusions with any considerable degree of certainty. 

4. The Influence of Temperature on the Conductance of the Ions. 
As is shown in Table XLII, with increasing temperature the conductance 
of the ions increases, and this irtcrease is the more nearly proportional 
to the increase in the fluidity of the solvent, the lower the conducting 
power of the ion. In the case of the acetate ion, the conductance is 
everywhere proportional to the fluidity of water from 0° to 156°, which 
is the entire interval over which the viscosity of the solvent has been 
measured. In the following table are given the ratios of the fluidity of 
water to the conductance of the acetate ion from 0° to 156°.^° 

TABLE XLIV. 

Ratio of the Fluidity of Water to the Conductance of the Acetate 
Ion at Different Temperatures. 

Temp 0° 18° 25° 50° 75° 100° 128° 156° 

^CHCOO- "" ^'^^ ^'^^ ^'^^ ^'^^ ^"^^ ^"^^ ^'^^ ^'^^ 

It is evident that, in dilute solutions, the conductance of the acetate ion, 
and presumably therefore its speed, is directly proportional to the fluidity 
of the solvent. 

Since the conductance of the acetate ion is proportional to the fluidity 

" Johnston, loo. cit. 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 123 

of water up to 156°, we may assume, in the absence of experimental 
data, that it remains proportional at higher temperatures. In order, 
therefore, to compare the conductance of the different ions with the 
fluidity of water, we may compare the conductance of these ions with 
that of the acetate ion whose values are known up to 306°. The ratio 
of the conductances of the various ions to that of the acetate ion is given 
in Table XLV." 

TABLE XLV. 

Influence of Temperature on the Conductance of Various Ions 
Relative to That of the Acetate Ion. 

Ion Conductance at temperatures : — 

0.0° 18° 25° 50° 75° 100° 128° 156° 218° 306° 

K* 1.99 1.87 1.83 1.72 1.66 1.58 1.54 1.50 1.32 1.18 

Na^ 1.28 1.26 1.25 1.22 1.20 1.19 1.19 1.18 1.15 1.11 

NH/ .... 1.98 1.86 1.83 1.72 1.66 1.59 1.55 1.52 1.37 1.30 

Ag* 1.62 1.57 1.54 1.51 1.49 1.45 1.43 1.42 1.29 .. 

CI- 2.02 1.89 1.85 1.73 1.67 1.59 1.54 1.51 1.32 1.18 

NO3- 1.99 1.78 1.73 1.55 1.46 1.37 1.30 1.25 1.21 .. 

H* 11.82 9.08 8.58 6.95 5.88 4.95 4.23 3.68 2.79 1.82 

OH- 5.17 4.95 4.71 4.24 3.75 3.38 3.07 2.81 2.08 1.62 

In determining the conductance of the various ions, it is of course 
necessary to assume values for the transference numbers of one pair of 
ions. In the case of potassium chloride, the transference number is very 
nearly 0.5 and at higher temperatures it appears to approach this value 
as a limit. It has been assumed, therefore, that at temperatures above 
100° the transference number of the potassium and chloride ions is 0.5. 
This assumption, moreover, is justified by the fact that, as the tem- 
perature increases, the transference numbers of all ions appear to 
approach one another. In the above table the ionic conductances at 
the higher temperatures are based upon this assumption. 

The relation between the ionic conductances and the temperature is 
shown in Figure 21, where the conductances relative to the acetate ion are 
plotted as ordinates and the temperatures as abscissas. Since the con- 
ductance of the acetate ion is proportional to the fluidity of the solvent, 
it follows that the ordinates will be proportional to the ratio of the ionic 
conductances to the fluidity of the solvent. On examining the figure, 
it will be seen that the greater the value of the conductance of an ion, 
the less does the conductance increase as the temperature increases. 

^i 

That is, the ratio decreases with increasing temperature and de- 

^ac 

" Kraua, loc. cit. 



124 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

creases the more, the greater the value of the ratio. In other words, 
these ratios appear to approach unity, as a limit at high temperatures. 
The conductances of all ions, therefore, appear to approach that of very 
slowly moving ions. For example, at 0° the conductance of the hydrogen 
ion is 11.82 times that of the acetate ion, while at 306° it is only 1.82 
times that of this ion. At 0° the conductance of the potassium ion is 
1.99 times that of the acetate ion, while at 306° it is only 1.18 times that 
of this ion. At 0° the conductance of the sodium ion is 1.28 times that 
of the acetate ion, whereas at 306° it is only 1.11 times that of the same 



■ 3 


































2 H+ 

S 


\ 
































\ 






























a g 

o 




\ 




























-JJ 




\ 


\ 


























o 

& OH- 






\ 


\ 
























^ 






"N 


\ 






















S 




^- 








^ 


^ 


















i i 








■^ 




^^ 






\ 


_^ 












1 i' 


















~- 


— 









-___ 




















o NO.- 


-^ 


■=^rr;-. 




: 


'^ZTiz: 












-.._ 






' 


- — - 


i Na+ 
■3 


<. 































o 



Temperature. 



300' 



Fig. 21. Showing the Relative Change of Ionic Conductances with Temperature. 



ion. It is evident, therefore, that as the temperature increases the speeds 
of the different ions approach a common value. With the exception of 
the nitrate ion, the curves for the ionic conductances do not intersect. 
At low temperatures, however, the relative conductance of the nitrate 
ion, with respect to that of the acetate ion, decreases much more rapidly 
than it does for other ions having the same conducting power. At 0° 
the ratio of the conductance of the nitrate ion to that of the acetate 
ion is 1.99, whereas at 25° it is only 1.73. In the case of the potassium 
ion at the lower temperature, the ratio is also 1.99, but at 25° it is 1.83. 

These results have an important bearing on our conceptions as to 
the nature of the conducting particles, particularly as regards the effect 
of temperature on the speed of these particles. As has been shown by 



THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 125 

means of transference experiments, the ions are hydrated in water. In 
order to account for the fact that the speeds of the different ions at 
higher temperatures approach one another, it might be assumed that the 
hydrates break down at higher temperatures, but this assumption would 
not be in harmony with certain facts. Since the conductance of the 
slowly moving ions changes in direct proportion to the fluidity of the 
solvent as the temperature increases, it is reasonable to assume that the 
relative dimensions of the ion complex remain practically constant. If, 
therefore, the speed of the more rapidly moving ions approaches that of 
the more slowly moving ions at higher temperatures, it points to a slow- 
ing up of the more rapidly moving ions as the temperature increases. 
This corresponds to a greater relative resistance to their motion, which 
can only be interpreted as due to an increase in the dimensions of the 
ion-complex. In other words, as the temperature increases, the hydra- 
tion of the more rapidly moving ions increases, which tends to reduce 
their speed relative to that of more slowly moving ions. 

If the hydration of the ions is due primarily to electrical forces acting 
between the ions, which are charged, and the surrounding solvent mole- 
cules, which have an electrical moment, then we should expect that, as 
the dielectric constant of the medium decreases, the size of the complex 
will increase, since in a dielectric medium the force is inversely propor- 
tional to the dielectric constant. For this reason we should expect the 
relative speeds of ions in non-aqueous solvents of low dielectric constant 
to approach one another much more nearly than they do in water. This 
appears to be the case. Moreover, this is also in harmony with the fact 
that in the case of very large ions, in other words, in the case of ions 
which have a low conducting power, the conductance in different sol- 
vents, as well as at different temperatures, is very nearly proportional to 
the fluidity of the solvent. We may conclude, therefore, that the hydra- 
tion of the ions increases, or, including non-aqueous solvents, that the 
solvation of the ions increases with the temperature because of a decrease 
in the dielectric constant of the medium. It is not to be assumed, how- 
ever, that the dimensions of the ions in different solvents are controlled 
entirely by the dielectric constant. The solvent may combine chemi- 
cally with a given ion to form a complex, which ion in turn may have 
associated with it additional solvent molecules, due to electrical inter- 
action between this ion and the solvent. We should expect this to be 
the case with silver ions which form an extremely stable complex with 
ammonia. Even in aqueous solutions, the silver ion forms a complex 
Ag(NH3)2* with ammonia. This may account for the relatively low 
conducting power of the silver ion in liquid ammonia solution. Whereas, 



126 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

for example, the conductance of the lithium ion in ammonia is 3.36 times 
that of the lithium ion in water, that of the silver ion in ammonia is only 
2.15 times that in water. So, also, we find that the ammonium ion in 
ammonia has a conductance of only 2.03 times that of the ammonium ion 
in water, indicating the formation of relatively large complexes. In this 
connection it may be pointed out that the ammonium salts form with 
ammonia saturated solutions whose vapor pressures are extremely low. 
For example, the vapor pressure of a saturated solution of ammonium 
nitrate in ammonia is one atmosphere at 26°. 

If the complexity of the ions increases with the temperature, we 
should expect that at higher temperatures the viscosity would be in- 
creased more largely for a given addition of salt than at lower tem- 
peratures. This, again, corresponds with observations on the viscosity 
of solutions. The change of viscosity due to a given addition of 
salt increases as the temperature rises, and this increase appears to be 
the greater the higher the temperature. It is to be noted, also, that the 
increase in viscosity due to the addition of electrolytes is much greater 
than that due to the addition of non-electrolytes, except in the case of 
non-electrolytes which have very large molecules. In general, as has 
already been pointed out, the viscosity effect is the greater the lower 
the dielectric constant of the solvent. In solvents of very low dielectric 
constant, the viscosity of some solutions becomes so great, at high con- 
centrations, that they often become practically solid. 

5. The Influence of Pressure on the Conductance of Electrolytic 
Solutions. As we have seen, the conductance of the ions is a function 
of the viscosity of the solution. As the hydrostatic pressure on a solu- 
tion is increased, its viscosity changes, the sign and magnitude of this 
change being dependent upon the nature of the solvent medium and 
upon the concentration of the solution in question. The effect of pres- 
sure on the viscosity of solutions in water, as well as the effect upon 
water itself, has been measured by Cohen.^' In Figure 22 are shown 
the percentage changes of viscosity for pure water at different pressures 
and temperatures. From an inspection of the figure it will be seen 
that with increasing pressure the viscosity of water decreases markedly. 
As the temperature rises, however, the viscosity effect diminishes and 
it is evident that at higher temperatures the effect changes sign. From 
the form of the curves at 15° and 23° it is evident that at higher pres- 
sures the curves for the viscosity effect will pass through a minimum and 
that ultimately, therefore, the viscosity change will change sign the 
viscosity increasing with increasing pressure. In non-aqueous solvents 

"Cohen, Wied. Ann. i5, 666 (1892). 



THE CONDUCTANCE OF SOLUTIONS— VISCOSITIES 



127 



the viscosity increases with increasing pressure, as was found by Ront- 
gen ^* and Warburg and Sachs ^® for ether and benzene, and by Cohen 
for turpentine. In general, the viscosity effect in non-aqueous solvents 
is greater than that in water, and, as we shall see below, the effect is 
the greater the greater the viscosity of the medium. 

The pressure-viscosity effect in solutions is a function of the con- 
Pressure in Atmospheres. 
O ZOO kOO eOO 800 lOOO 



1 


^. 














\^ 


^.A 




zi" 






i^ 


\ 


^ 












\ 


1 


f ^^**"*^ 

^ 








P 


\ 








— s/^ 


O 


>..? 


\ 












m * 




\ 










-1-3 




\ 










Ph ,5 






\ 








fi 






\ 














^ 


\io 







Fio. 22. Showing the Influence of Pressure on the Viscosity of Water at Different 

Temperatures. 

centration, as was shown by Cohen. In Figure 23 are shown curves 
for the viscosity change of solutions of sodium chloride in water at 2° 
and 14.5°. The broken line curves relate to the lower temperature. 
The concentrations of the various solutions are indicated on the figure. 
With increasing concentration of the solution, the viscosity decrease, due 
to a given increase in pressure, diminishes and ultimately changes sign; 
that is, with increasing pressure, the viscosity of the solution increases. 
The lower the temperature, the greater the influence of a given pressure 

"Rontgen, Tfied. Ann. 22, 510 (1884). ,_^^,. 
" Warburg and Sachs, Wied. Ann. 23, 518 (1884), 



128 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

change upon the viscosity, but at higher concentrations the effect of 
temperature diminishes greatly. 

Pressure in Atmospheres. 



4 






A 


ZS,T% 


.? 






// 
/ / 




? 




J' 

// 


/ 




/ 


y 


// 


y 


j/?*^ 


1 

^0 


z 


^ 


_-- 


:S% 


'^ i 


a' 




10 6i 


W 


1 

(U 


\ 
\ 

\ 




-, 


t8% 


3 


\ 

\ 
\ 




■^ 


[ 0% 


« 




V 

\ 

\ 






S 




\ 
\ 
\ 


\ 




« 






\ 


i 



Fig. 23. Showing the Influence of Pressure on the Viscosity of Aqueous Sodium 
Chloride Solutions at Different Concentrations. 

The change in the viscosity of a solution with pressure will obviously 
have an influence upon the conductance of the solution. The viscosity 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 129 

effect, however, is not the only one involved. As Tammann has shown,^" 
the conductance-pressure coefficient is the resultant sum of four effects; 
namely, the volume change of the solution due to pressure change, the 
change in the mobility of the ions due to the viscosity change of the 
solution, the change in the ionization of the electrolyte, and finally the 
change in the conductance of the solvent medium, which, as a rule, is due 
to a small quantity of electrolyte present as impurity. The conductance- 
pressure coefficient, therefore, is given by the equation: 

(43) lA3l_lAv J.Aqp lAy ,X;j^A/ 

X Ap V Ap "^ qp Ap "*" Y Ap "^ X y' Ap 

where I is the conductance of the solution due to the electrolyte, I' that 
due to the solvent medium, y is the ionization of the electrolyte and y' 
that of the solvent medium, and cp is the ionic resistance; that is to say, 
the reciprocal of the ionic mobility. In the equation, therefore, the first 
term of the right-hand member measures the conductance change due 
to the volume decrease of the solution; the second term measures the 
conductance change due to the viscosity change of the solution ; the third, 
the conductance change due to the ionization change of the electrolyte; 
and the last term, the conductance change due to the ionization change 
of the solvent medium. By suitably choosing the condition of the solu- 
tion, it is possible to minimize the value of various of the terms enter- 
ing into this equation, and thus make apparent the effect of the various 
factors on the conductance of the solution due to pressure change. 

Let us examine first the typical form of the conductance-pressure 
curves in the case of aqueous solutions of 0.01 N KCl. In Figure 24 ^'■ 
are represented values of the ratio of the resistance of the solution, i?„, 
under a pressure of p kilograms per square centimeter to the resistance 
Rp=x under a pressure of one atmosphere at a series of temperatures. It 
will be observed that as the pressure increases the resistance of the solu- 
tion decreases initially. As the temperature rises, the value of the 
decrease due to a given pressure change diminishes. At high pressures 
the isotherms exhibit a minimum. The higher the temperature, the lower 
the pressure at which the minimum occurs. It is evident that at suffi- 
ciently high temperatures the minimum will disappear and the resistance 
of the solution will increase throughout with increasing pressure. This 
has been found to be the case with strong electrolytes, such as sodium 
chloride in aqueous solution. 

In solutions of strong binary electrolytes, the ionization at a con- 
centration of 0.01 N is so high that but little change is to be expected in 

=• Tammann, Ztschr. f. pJiya. Chem. 27, 458 (1898). 
"Kdrber, Ztschr. /. pliys. Chem. 67, 222 (1909). 



130 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

its value as a result of pressure change. The third term of the right- 
hand member of Equation 43 may therefore be neglected. The fourth 
term, likewise, may be neglected at this concentration, since the con- 
ductance of the pure solvent is negligible in comparison with that of the 
solution. The observed conductance change of solutions, under these 
conditions, therefore, is due to the first two terms. The value of the first 




Fia. 24. Showing the Influence of Pressure on the Resistance of 0.01 N Aqueous 
KCl Solutions at Different Temperatures. 

term of the right-hand member may be calculated from the data of 
Amagat on the compressibility of pure water, since the compressibility 
of an 0.01 N solution will not differ appreciably from that of pure water. 
If the first term of the right-hand member is transposed, we have the 
equation: 

^ (jpAp XAp vAp' 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 131 

from which equation the effect of pressure upon the conducting power of 
the ions may be determined. In a solution at a concentration of 01 N 
the effect of pressure on the viscosity will not differ materially from 
that on the pure solvent. It might be expected that the effect of pressure 
on the conductance of the ions would vary inversely as the viscosity change 
of the solution. Indeed, Tammann, on comparing the conductance-pres- 

Pressure. 
Sf> MU) tjfio tepo z^ 3qo0 j^ g ,«, 




Fig. 25. Comparison of the Influence of Pressure on the Conductance and the 
Fluidity of Dilute Aqueous NaCl Solutions at Different Temperatures. 

sure effects as calculated according to Equation 44 for 0.1 N sodium 
chloride with the measured viscosity effects of Cohen, found almost an 
exact correspondence as may be seen from Figure 25.^^ The points on 
this figure represented by combined cross and circle are measured vis- 
cosity values of Cohen, while the curves represent the values of the vis- 
cosity effect as determined from conductance measurements according to 
Equation 44. Measurements by Korber,^^ while confirming the results 
of Tammann for sodium chloride, show that the viscosity-conductance 
effect due to pressure in the case of different electrolytes is a function 

22 Tammann, Wied. Ann. 69, Y73 (1899). 
»Korber, Ztschr. f. phys. Chem. 61, 212 (1909). 



132 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



Pressure. 
500 1000 1500 2 000 2500 5000^3 




0.82 

Fig. 26. Influence of Pressure on the Resistance of 0.01 N Solutions of Different 

Salts in Water at 19.18°. 

of the nature of the ions and that the correspondence found for sodium 
chloride is purely accidental. p 

In Figure 26 are represented values of the ratio ^-2- for aqueous 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 



133 



Pressure. 

fOOQr S^O ^000 1500 3000 2500 3000!^ 

Cm-* 
Nal 




-0X)9 



Fia. 27. Showing the Influence of Pressure on the Resistance Coefficients for 
Aqueous Solutions of Various Electrolytes. 



134 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 
• solutions of various electrolytes at a concentration of 0.01 N at a tem- 
perature of 19.18°, while in Figure 27 ^* are shown values ^^ ~-^ ^^ ''^'- 

culated from the measured values of -^, according to Equation 44. 

As stated above, the curve for sodium chloride corresponds with the 
viscosity curve of pure water as determined by Cohen. It will be seen, 
however, that the curves for other electrolytes differ from that of sodium 
chloride and that, therefore, in these cases the pressure effect upon the 
ions is not directly proportional to the viscosity change of the solution. 
In the case of potassium chloride the conductance evidently increases 
slightly more than corresponds to the viscosity change of the solution, 
while for lithium chloride and hydrochloric acid the conductance increase 
due to increasing pressure is enormously greater than the viscosity change 
of the solution. On the other hand, in the case of potassium bromide, 
sodium bromide, potassium iodide, and sodium iodide the conductance 
change of the electrolytes is much smaller than the corresponding vis- 
cosity change of the solution. Manifestly, the change in the speed of 
the ions with pressure change is dependent not only on the viscosity of 
the solvent medium, but also on other factors. What these factors are, 
we do not know with certainty, but it appears probable that the speed 
of the ions is affected by a change in their effective size. Such an effect 
will obviously be a property of the ions themselves, which is in accord- 
ance with Korber's observations. However we may interpret these 
results, it is obvious that the speed of the ions in a dilute aqueous solution 
is not determined primarily by the viscosity of the solution, although the 
viscosity is an important factor. 

According to Equation 43, the value of the ratio — ^ varies as a 

function of concentration. In Figure 28 2= are shown values of the ratio 

^-^ for sodmm chloride in water at 19.18° at a series of concentrations. 

At the highest concentrations the resistance of the solution increases 
throughout with increasing pressure. This is in accord with Cohen's 
observations on the viscosity of sodium chloride solutions, which, at 
higher concentrations, exhibit a marked viscosity increase. As the con- 
centration of the solution decreases, the curves exhibit a minimum 
Initially, with increase in pressure, the resistance of the solution decreases^ 

=* Korber, loc. cit., p. 227. 
'' lUd., loc. cit., p. 234. 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 



135 



Pressure. 
1 500 1000 1500 2000 3500 300 Ka 
' ' ' ' Cm.2 




Fig. 28. Showing the Influence of Pressure on the Resistance of Sodium Chloride 
Solutions at Different Concentrations at 19.18°. 



while at higher pressures the resistance of the solution increases. In 
this case, again, the general form of the curve corresponds to the viscosity 



136 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

effects of the solution. As the concentration decreases, the minimum 
point is displaced toward higher pressures, and the curves approach one 
another. Thus the curves at 0.1 N and 0.01 N differ but little. This is 
due to the fact that below a concentration of 0.1 N the ionization of the 
electrolyte is so great and the concentration so low that the viscosity- 
effects could not differ materially from those in pure water. At lower 
concentrations, namely at 10"^ N and 10"* N, the minimum disappears 
and the pressure effect becomes very large, the curves becoming the 
steeper, the lower the concentration of the solution. This divergence of 
the curves at very low concentrations is due to the effect of pressure on 
the conductance of the solvent medium; namely, to the fourth term in 
Equation 43. In the limit, these curves approach the dotted curve shown 
in the figure, which is that of the solvent medium. 

We have still to consider the case in which the third term of Equation 
43 becomes an effective factor. This will obviously be the case with 
solutions of weak electrolytes. The ionization of an electrolyte, if the 
mass-action law holds — and this is in general the case with weak electro- 
lytes in aqueous solutions — is determined by the value of its ionization 
constant K. According to the Planck equation, we have: 

(Uo.) d log ii: _ Av 

^^^^' dp - RT- 

According to Tammann, the value of Kv is negative, so that as the result 
of pressure increase the value of the ionization constant K increases and 
with it the value of the ionization y. In the case of weak electrolytes, 
at intermediate concentrations and lower temperatures, the first three 
terms of Equation 43 have the same sign, and consequently the resist- 
ance of solutions of weak electrolytes should decrease with increasing 
pressure much more largely than that of solutions of strong electrolytes 
under otherwise the same conditions, and the decrease should be the 
greater the weaker the electrolyte and the greater the value of hv. The 
first investigations in this direction were carried out by Fanjung.^" 
Measurements on 0.1 N acetic acid were carried out by Tammann up to 
pressures of approximately 4000 kilograms per square centimeter. In 

the following table are given values of the ratio ~P- for acetic acid 

R'p=i 
at 20.14°." 

In the case of ammonia, which has approximately the same ionization 
constant as acetic acid, the pressure effect is even greater than in that of 

'"Fanjung, Ztsehr. f. phys. Chem. H, 6T3 (1894). 
"Tammann, Wied. Ann. 69. 770 (1899). 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES 137 

acetic acid, since the value of Aw for ammonia is more than twice that 
of acetic acid. 

TABLE XLVI. 

Relative Resistance of 0.01 N Solutions of Acetic Acid in Water 
AT 20.14° at Different Pressures. 



Pkg. 



cm.^ 

1 

500 
1000 
1500 
2000 
2500 
3000 
3500 
4000 



Rp=i 

1.000 
0.855 
0.738 
0.650 
0.582 
0.526 
0.487 
0.447 
0.410 



The influence of pressure upon the conductance of electrolytes is 
brought out more clearly by representing the conductance-pressure coeflS- 



O _ 



Ph 



3 
-O 
d 
o 
O 




Fig. 29. Conductance-Pressure Coefficients for Electrolytes of Different Types as a 
Function of Concentration at a Pressure of 500 kg./cm.^. 
Curve 1, Weak Electrolytes. 
Curve 2, Moderately Strong Electrolytes. 
Curve 3, Strong Electrolytes. 

cient as a function of the concentration of the solution, the pressure 
remaining constant. In Figure 29 ^^ Curve 1 represents the pressure 

2s Tammann, Ztschr. f. pliya. Chem. n, 729 (1895). 



138 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

coeiScient of weak electrolytes as a function of their concentration at a 
pressure of 500 kg./cm.^ The curve actually corresponds very closely with 
that of acetic acid in water at this pressure. As Tammann has shown, 
it follows from the Planck equation that at low concentrations and for 
relatively small values of the constant K the ionization change, due to 
increasing pressure, increases with increasing concentration, until a prac- 
tically constant value is reached. The conductance-pressure coeffi- 
cient increases with increasing concentration of the weak electrolyte 
up to a concentration of aboi^t 10"^ normal for electrolytes whose con- 
stant is below 10"*. At higher concentrations the ionization change due 
to pressure change remains practically constant. However, at higher 

concentrations the value of - -v— decreases, while the value of — r^ 

V Ap (p Ap 

decreases and ultimately changes sign, as follows from Cohen's observa- 
tions on the viscosity of aqueous salt solutions. Therefore, the con- 
ductance-concentration curves, and consequently the curves for the coeffi- 
cient, exhibit a very flat maximum. In the case of solutions of strong 

electrolytes, the term --r-i- has inappreciable values at concentrations 
Y ixp 

below 10"^ normal, and has only very small values at much higher con- 
centrations. In dilute solutions, therefore, the pressure coefficient has 
very nearly a constant value, independent of concentration. At higher 
concentrations, however, the value of the coefficient decreases, owing to 

the diminution in the value of - ^ and owing to an ultimate change in 

the sign of the viscosity effect at higher concentrations of the electrolyte, 
as was found by Cohen. Electrolytes of intermediate strength exhibit 
a type of curve intermediate between these two extreme types, as repre- 
sented by Curve 2. In this case the value of the coefficient increases 
with increasing concentration of the solution at lower concentrations 
owing to the increasing ionization of the electrolyte. Ultimately, how- 
ever, the effect of the viscosity change makes itself felt, the curve passes 
through a maximum, and thereafter falls with increasing concentration. 
At very low concentrations the viscosity-pressure coefficient has actually 
been found to increase and approach large values due to the effect of the 
fourth term in the right-hand member of Equation 43. This increase 
in the coefficient, as was shown by Tammann,2» is due to the increased 
ionization of the solvent medium. 

The limiting value which the coefficient i^ approaches at low con- 

"•Tammann, ZtecJir. J. phys. Ohem. 27, 464 (1898). 



THE CONDUCTANCE OF SOLUTIONS—VISCOSITIES 139 

centrations, assuming that the conductance of the solvent is zero, or has 
been otherwise corrected for, differs for different electrolytes, and is, in 

general, the greater, the greater the value of . Thus the limit ap- 

proached for hydrochloric acid at a pressure of 3000 kilograms per square 
centimeter is approximately 17 per cent, while that of sodium chloride 
is approximately 8 per cent and that of potassium chloride 9 per cent. 

Since in dilute solution the effect due to - i— is the same as that in pure 

V Ap 

water, it follows that these differences are due to differences in the vis- 
cosity effect as illustrated in Figure 28. In the case of hydrochloric 

acid, the value of •=- -r— passes through a flat maximum at a concentration 

in the neighborhood of 0.5 normal. 

In non-aqueous solutions the order of the viscosity effects differs 
from that in aqueous solutions, chiefly owing to the fact that with in- 
creasing pressure the viscosity of the solvent medium increases and con- 
sequently the speed of the ions is reduced with increasing pressure. In 

Figure 30 ^° are shown values of the ratio for solutions of 0.002 N 

Kp=i 

tetramethylammonium iodide and 0.1 N malonic acid in ethyl alcohol. 
As was the case with water, the curve for weak electrolytes lies below 
that for strong electrolytes. With increasing temperature, however, the 
order of the curves is reversed with respect to their order in water; that 

R„ 

is, the ratio — — decreases both in the case of strong and weak electro- 
Rp=i 

lytes. The curves are very nearly linear for solutions of strong electro- 
lytes but are convex toward the axis of pressures for solutions of weak 
electrolytes. This form of the curve is accentuated in solutions in sol- 
vents of high viscosity; as, for example, amyl alcohol, for which values of 

2_are represented in Figure 31.'^ In this case, the curves for malonic 

Rp=i 

acid at higher temperatures exhibit a minimum, while the curves for 
tetramethylammonium iodide are distinctly convex toward the axis of 
pressures. It is evident that at pressures beyond 3000 kilograms per 
square centimeter the curve for malonic acid in ethyl alcohol would 
likewise pass through a minimum. The observed phenomena in non- 

»o Schmidt, ZtscJir. f. phys. Chem. 75, 319 (1910). 
=1 Hid., loc. cit., p. 320. 



140 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

aqueous solutions may be accounted for in the same manner as those for 
aqueous solutions. The difference in the form of the curves for various 
electrolytes in the two cases arises chiefly as a result of the difference 



C» ^Ql>i.g9 




1000 2000 

Pressure in kg./cm." 



3000 



Fig. 30. Showing the Influence of Pressure on the Resistance of 0.002 N Solutions 

S^.u , A^'^u .'''^"S^^"'"™ ^^^"^^^ (above) and 0.1 Malonic Acid (below) in 
Jithyl Alcohol at Different Temperatures. 



in the sipi and magnitude of the viscosity pressure effect and in the value 
of the ionization of the dissolved electrolytes. In solvents of lower 
dielectric constant, the typical salts behave like electrolytes of inter- 
mediate strength. At a given pressure, with increasing concentration of 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES Ul 

200 ^gcgo 




1000 2000 

Pressure in kg./cm.^ 



3000 



Fig. 31. Showing the Influence of Pressure on the Resistance of Solutions of Tetra- 
methylammonium Iodide (dotted) and Malonic Acid (continuous) in Amyl 
Alcohol at Different Temperatures. 

the electrolyte, the ratio — ^-, due to the increased ionization of the 

electrolyte, increases from values less than unity to greater values which 
are in general less than unity. At still higher concentrations, however, 



142 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the increasing viscosity effect overbalances the effect of increased ioniza- 
tion and the curve passes through a maximum. In solutions of weak 

K 

electrolytes the ratio -^-^ increases rapidly with increasing concentration 

of the electrolyte, due to increased ionization, and, for very weak electro- 
lytes, particularly at low temperatures, passes through unity to greater 
values. Here, again, at sufficiently high concentrations, the curve may 
pass through a maximum, owing to the ultimate predominance of the 
viscosity effect. From his measurements, making the assumption that 
the Planck equation holds as well as certain other assumptions, Schmidt 

has calculated the value of — ^, the viscosity ratio, due to pressure, for 

potassium iodide, sodium iodide and tetramethylammonium iodide in 
alcohol. He found that this ratio increases markedly with the pressure. 
In the case of potassium iodide and sodium iodide the increase is very 
nearly the same, being from 1.0 to 2.34 for 0.02 N solutions and a pres- 
sure change from 1 to 3000 atmospheres. In the case of tetramethyl- 
ammonium iodide the ratio — — increases si)mewhat more than for the 

other two electrolytes measured. This indicates that the viscosity effect 
in alcohol, similar to that in water, is a property of the ions. It appears, 
however, that the effects in the case of different ions are much more 
nearly the same in non-aqueous solutions than in water. This is as 
might be expected, since in solvents of low dielectric constant the ionic 
conductances themselves differ much less than in water. Schmidt has 
also calculated the value of the ionization y at different pressures and 
has found that the ionization increases with increasing pressure. 

That the pressure effect is intimately related to the viscosity of the 
solution is clearly indicated by the fact that the order of the effects in 
different solvents corresponds to the order of the viscosities of these 
solvents. The higher the viscosity of the solvent, the greater is the ratio 

p-^ for a given pressure change. In the majority of solvents Schmidt 

found that this ratio might be expressed as a function of the pressure by 
the equation: 

(45) log^=i3p, 

where p is a constant. This equation was found to be particularly ap- 
plicable at higher temperatures, In other cases it was necessary to add 



THE CONDUCTANCE OF SOLUTIONS-VISCOSITIES I43 

a quadratic term to the right-hand member of the equation. In the case 
of non-associated liquids the value of p may be expressed in terms of 
the viscosity of the solvent by means of the equation: 

(*6) 13 = 0.000106 + 0.00561 q), 

where cp is the viscosity of the solvent. In the following table are given 
values of the viscosity (p, together with the measured values of |3 and 
those calculated according to Equation 46.^^ 

TABLE XLVII. 

Relation Between the Viscosities op Different Solvents and 
THE Pressure Effects. 

Normal solvents. 

Solvent q) P P calc. 

Anisaldehyde 0.056 O.O342O O.O342O 

Benzylcyanide 0.022 O.O3234 O.O3229 

Nitrobenzene 0.020 O.O3217 O.O32I8 

Furfurol 0.017 O.O3204 O.O32OI 

Benzaldehyde 0.016 O.O3I94 O.O3I96 

Acetic anhydride 0.010 O.OglTS O.O3I62 

Acetone 0.003 O.O3IO6 O.O3I23 

Associated solvents. 

Glycerine 7.0 O.OgSOO O.OgOS 

Isoamyl alcohol 0.042 O.O3I78 O.O3342 

Ethyl alcohol 0.012 O.O3O95 O.O3I73 

Methyl alcohol 0.006 O.O3O78 O.O3I4O 

The calculated and observed values of P agree very well for the non- 
associated solvents, but in the case of the associated solvents there is a 
wide discrepancy between the two. A very simple relation thus exists 
between the viscosity and the pressure effect in the case of normal sol- 
vents, while in the case of associated solvents the relation is much more 
complex. This is as might be expected, for in associated solvents a 
change in the complexity of the solvent molecules doubtless accompanies 
any pressure change. It is clear that the difference in the nature of the 
pressure effects in water and in non-aqueous solvents is chiefly due to the 
difference in the viscosity effects in these cases. 

" Schmidt, loc. cit., p. 334. 



Chapter VI. 

The Conductance of Electrolytic Solutions as a Function 

of Temperature. 

1. Form of the Conductance-Temperature Curve. The limiting 
value of the conductance is a function of the viscosity of the solvent, and 
consequently of the temperature also. The conductance of the more 
slowly moving ions is very nearly proportional to the fluidity of the 
solvent over such ranges of temperature for which viscosity data are 
available. The conductance of the more rapidly moving ions increases 
relatively less with the temperature than does that of the more slowly 
moving ions, and this effect is the more marked the greater the con- 
ductance of the ions. 

In considering the conductance of solutions at higher concentrations, 
it is necessary to take into account another factor, namely the change 
in the ionization of the electrolyte. The observed conductance change is 
therefore the resultant effect due to the change in the viscosity of the 
solution and to the change in the ionization of the electrolyte. While, 
with increasing temperature, the viscosity decreases and the conduct- 
ance consequently increases, the ionization in general decreases and the 
conductance of the electrolyte decreases in consequence. Since these two 
factors affect the conductance in opposite directions, it follows that the 
resultant effect of temperature on the conductance will depend on the 
relative magnitude of the ionization and the viscosity effects; and, in 
general, with increase in temperature the conductance of a solution may 
either increase or decrease. At ordinary temperatures, the conductance 
of many solutions increases with the temperature, and it was formerly 
assumed that a positive temperature coefficient was a characteristic 
property of electrolytic solutions. We now know, however, that this is 
not the case and that the temperature coefficient of solutions may be 
either positive or negative and that, in a given solvent, the temperature 
coefficient is a function of the temperature as well as of concentration, 
and that the sign of the temperature coefficient may change with tem- 
perature as well as with concentration. 

Considering, first, the conductance as a function of temperature, the 
concentration remaining fixed, it is found that, in general, the con- 
ductance increases with the temperature at low temperatures; but as the 

144 



SOLUTIONS AS A FUNCTION OF TEMPERATURE I45 

temperature rises, the temperature coefficient decreases. The conductance 
curve is therefore concave toward the axis of temperatures. If the tem- 
perature is carried sufficiently high, the conductance passes through a 
maximum after which it decreases, the negative temperature coefficient 
increasing as the temperature rises. Experiments of this kind were first 
carried out by Sack,^ who found that, in solutions of copper sulphate 




-6O -40 -20 O ZO 40' 60 80 100 iZO 

Temperature. 

Fig. 32. Conductance-Temperature Curves for Various Electrolytes in 
Liquid Ammonia. 

the conductance passes through a maximum in the neighborhood of 128°. 
For solutions of strong binary electrolytes in water, however, the maxi- 
mum lies at much higher temperatures. 

Before proceeding to a detailed discussion of aqueous solutions, we 
may consider solutions in other solvents. The conductances of a con- 
siderable number of solutions in ammonia have been measured and a 
maximum has been found in all cases.^ The form of the curves will be 

•Sack, Wied. Ann. d. Pliys. J,S, 212 (1891). 

2 Franklin and Kraus, Am. ahem. J. H, 83 (1900). 



146 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

evident from Figure 32. As a rule the maximum lies in the neighborhood 
of 25° C but the temperature of the maximum is a function of concen- 
tration and with increasing concentration the maximum is displaced 
toward lower temperatures. The curves for different electrolytes are 
similar, indicating that the underlying phenomenon is the same in all 
cases. As the critical temperature is approached, the conductance ap- 
proaches a very low value, and it appears as though the curve would cut 
the axis of temperatures at a point near the critical temperature. The 
conductance, however, does not, in fact, fall to zero at the critical point, 
but has appreciable values at temperatures much above that point. The 
phenomenon in the neighborhood of the critical point will be discussed 
in detail in another section and need not be further considered here. It 
may be stated, however, that the property of forming conducting solu- 
tions with electrolytes is not peculiar to the liquid state but is one com- 
mon to fluid systems. 

The form of the conductance-temperature curve is the same in all sol- 
vents. The conductance of a considerable number of solutions in sul- 
phur dioxide has b9en measured ^ at higher temperatures and the curves 
obtained have a form which corresponds with those of ammonia solu- 
tions. In solutions of KI in methylamine the form of the curve differs 
slightly in that, at very high temperatures, the conductance appears to 
approach the axis of temperatures asymptotically. In the alcohols,* 
as well as in water,^ the conductance-temperature curves are of the same 
general type. 

2. Conductance of Aqueous Solutions at Higher Temperatures. 
In order to proceed with the discussion of this subject, it is necessary to 
have some notion as to the degree of ionization of the electrolyte in solu- 
tion. The degree of ionization of non-aqueous solutions at higher tem- 
peratures is unknown. In other words, we do not have a sufficient num- 
ber of measurements at a series of temperatures and concentrations to 
enable us to determine the value of A,, at these temperatures. For 
aqueous solutions, however, a large amount of material is available, 
having been obtained by A. A. Noyes and his associates,^ and from these 
data the effect of temperature on the ionization of salts becomes ap- 
parent. 

In the following table are given values of the equivalent conductance 
for potassium chloride at a series of temperatures and at the concentra- 
tions 0.08 and 0.002 normal. 

•Walden and Centnerszwer, Ztschr. 1. phiis. Chem 3D 54'' Iicin9\ 
'Kraus, Phys. Rev. 18, 40 and 89 (1904) ' IJ^»"^;. 

' Noyes, Carnegie Publication, No. 63, pp. 47, 103, and 266 
•Noyes, lOQ. oit. 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 147 

TABLE XLVIII. 
Conductance of KCl in HoO at Higher Temperatures. 



Concentration t 0° 


18° 


25° 


100° 140° 156° 218° 281° 306° 


0.08 N. A 72.3 


113.5 


— - 


341.5 455 498 638 723 720 


0.002 N. A 79.6 


126.3 


146.4 


393 534 588 779 930 1008 



It will be noted that at the higher concentration the conductance passes 
through a maximum somewhere between 281° and 306°. In the more 
dilute solution, a maximum has not been reached below 306°. This 
behavior is quite general in aqueous solutions and is found also in non- 
aqueous solutions. The lower the concentration, the higher the tem- 
perature of the maximum. 

For solutions of sodium chloride, the conductance-temperature curve 
is similar to that of potassium chloride, although for this salt the maxi- 
mum has not been reached at 306°, even at a concentration of 0.08 
normal. We have seen that, with increasing temperature, the conduct- 
ance of the sodium ion increases relatively more than that of the potas- 
sium ion. As a consequence, the maximum in the conductance curve is 
shifted to higher temperatures. In general, the higher the conductance 
of the electrolyte, the lower the temperature of the maximum and the 
lower the concentration at which the maximum will appear at a given 
temperature. 

For silver nitrate, the maximum lies somewhat lower than it does for 
potassium chloride, as may be seen from the following table: 

TABLE XLIX. 

Conductance of AgNOg in HgO at High Temperatures. 



Concentration 


t 


18° 


100° 


156° 


218° 


281° 


306 


0.08 N 


A 


96.5 


294 


432 


552 


614 


604 



The lower temperature of the maximum for silver nitrate is due, partly, 
to the abnormal manner in which the conductance of the nitrate ion 
changes as a function of the temperature and, partly, to the more 
rapid decrease in the ionization of silver nitrate with increasing tem- 
perature. 

The higher types of salts exhibit maxima which are more pronounced 
and which occur at lower concentrations and lower temperatures. In 
Table L are given values for barium nitrate and magnesium sulphate at 
0.08 normal. 



148 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE L. 

« 

Conductance of Ba(N0g)2 and MgSO^ in H2O at High Temperattjkes. 

Barium Nitrate. 

Concentration Temp, 
0.08 N A 



18° 100° 156° 218° 


281° 


81.6 257.5 372 449 


430 


Magnesium Sulphate. 




18° 100° 156° 


218° 


52 136 133 


75.2 



Temp. 
0.08 N A 

It will be observed that the maximum lies below 281° for barium nitrate, 
while for magnesium sulphate the maximum lies between 100° and 156°. 
The more complex the salt the lower the temperature and the lower the 
concentration at which the maximum appears. As we shall see presently, 
this is due chiefly to the fact that the ionization of salts of higher type 
falls off more rapidly with the temperature than does that of the binary- 
salts. For strong acids, the maxima lie at temperatures considerably 
below those of the binary salts. For hydrochloric acid the maximum 
lies in the neighborhood of 240° and for nitric acid in the neighborhood 
of 200° at a concentration of 0.08 N. 

The conductance-temperature curve of sulphuric acid, which is a 
dibasic acid, has a peculiar form, which has an important significance. 
Below are given values of the equivalent conductance for sulphuric acid 
at a series of temperatures at concentrations 0.002 and 0.08 normal. 





TABLE LI. 




Conductance of 


H2SO4 AT High Temperatures. 




Concentration 18° 25° 
0.002 N 353.9 390.8 
0.08 N 240 258 


50° 75° 100° 128° 156° 
501.3 560.8 571.0 551 536 
306 342 373 408 440 


218° 306° 
563 637 

488 474 



It will be observed that, at the higher concentration, sulphuric acid 
exhibits a relatively flat maximum at a temperature of about 250°, while 
at the lower concentration it exhibits a maximum at about 100° 'and a 
minimum at about 160°, after which the conductance again increases 
and presumably passes through a maximum at a temperature above 306° 
At still lower concentration the maxima and minima become more pro- 
nounced. As Noyes and Eastman ' pointed out, this behavior of sul- 
phuric acid appears to be due to the fact that ionization takes place in 
two stages according to the equations: 

' Noyes, loo. cit., p. 270. 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 149 

H,SO, = H- + HSOr 
HSO,- = H+ + SO,-- 

At the higher concentrations, the second ionization process has taken 
place to only a small extent and the form of the curve is largely due to 
the change in the ionization according to the first process, the maximum 
point occurring when the increased conductance of the ions due to tem- 
perature is just counterbalanced by the decreased conductance due to 
decrease in ionization. At the lower concentration the second ionization 
process is likewise involved. The second ionization corresponds to that 
of the weaker acid and the ionization according to this process falls off 
more rapidly with rising temperatiu-e, thus giving rise to the initial 
maximum. When the ionization according to the second process has 
been largely depressed, the curve thereafter depends chiefly upon the 
ionization according to the first equation. 

The ionization of strong electrolytes, apparently without exception, 
decreases with increasing temperatures; but at lower temperatures the 
rate of decrease is relatively small. In the case of the weak acids and 
bases the ionization increases between 0° and 40°, and thereafter de- 
creases rapidly at higher temperatures. In the following table are given 
values for the ionization constants of ammonium hydroxide and acetic 
acid.' The values represent averages for a number of concentrations. 
In general, the ionization constant is independent of concentration up 
to 0.1 normal. 

TABLE LIT. 

Ionization Constant X 10"* foh Ammonium Hydroxide and 

Acetic Acid. 

18° 25° 218° 306° 

NH.OH 17.2 18.1 1.80 0.093 

CH3COOH 18.3 — 1.72 0.139 

Initiaily there is a slight increase in the ionization constant, after 
which there is a sharp decrease at higher temperatures. Between 218° 
and 306° the constant oi ammonium hydroxide changes slightly more 
than that of acetic acid. Similar results have been obtained in the case 
of other weak acids. For example, the ionization constant of diketo- 
tetrahydrothiazole » at 0°, 18° and 25° is respectively 0.0711 X 10"% 
0.146 X 10-* and 0.181 X 10"*. Between 0° and 25° the constant of am- 
monium hydroxide varies between 13.91 and 18.06 X 10"*. It appears 

' Noyes, loc. oit., p. 234. 
» IMd., loc. cit., p. 290. 



150 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

that the change in the value of the constant is greater for the weaker 
electrolyte. 

The ionization constant for water itself is a function of the tem- 
perature. At ordinary temperature the constant has been variously 
determined, the values at 18° lying between 0.68 and 0.80, the lower 
value being probably the more nearly correct. 

In the following table are given values of the ionization constant of 
water at various temperatures up to 306°.^" 

TABLE LIII. 

Ionization Constant of Water at Diffeeent Temperatures. 

0° 18° 25° 100° 156° 218° 306° 

K„, X 10" .. . 0.089 0.46 0.82 48. 223. 461. 168. 

w 

The ionization constant of water thus increases very rapidly at lower 
temperatures and passes through a maximum not far from 218°. The 
large value of the ionization constant of water and the relatively low 
values of the ionization constants of the acids and bases at higher tem- 
peratures lead to a relatively large hydrolysis of the salts of anything 
but the strongest acids and bases, and it is not improbable that even 
salts of the strong acids and bases ultimately suffer hydrolysis at low 
concentrations at the highest temperatures. 

The increase in the ionization constant of the weak acids between 
0° and 40° may be related to the molecular changes which water under- 
goes within this temperature interval. Within this interval the density 
and specific heat of water are abnormal and within this temperature 
interval, also, the viscosity effects in solution, as well as the viscosity 
effects under pressure, exhibit abnormal relations, as has already been 
pointed out. An adequate explanation of these various phenomena, how- 
ever, appears not to exist. 

The ionization of different electrolytes in water at temperatures from 
18° to 306° are given in Table LIV at concentrations of 0.01 and 0.08 
normal. An examination of this table shows that the ionization of all 
electrolytes decreases markedly with the temperature, the decrease being 
the greater the higher the temperature and the higher the concentration. 
The ionization-temperature curves of different binary electrolytes corre- 
spond closely with one another, with the exception of the strong acids 
and silver nitrate. In the case of the last named salt, however, the 
ionization values at the highest temperatures are subject to large errors 

"> Noyes, loo. cit, p. 346. 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 



151 



•o "o 



^ 



CO 

"o 



.00 (rq r-i CO 
ci Oi ; o ! o CD 

Oi oo 05 as 00 



CO 



:<^ 



■00 



•U5 



•o 



« t>: I-) c^ 00 ■-! p 
"^' oi ; c^ ! ^ 00 ! i->^ 00 

Oi 00 03 05 00 00 00 



•o6 'i-i 'oi 'i-i 
■^ CO t-t 



(M 


t^ i-H 


t^ 


(N 00 


03 


03 05 


•^ 


en 05 



CO 
CO 
00 



s; 



CO 



■^ 






cq C^ CD !>: '^ 



d *-< ^ 

O CD 



T-HOO'-tOO^T-IOO^CO.-H.-HOO^^OOrHOO^OOT-too^OO^OO^OO^GOi-HOO 
CTiO PQ O OO PP p pp P PP PP PP PO pp PP PP PP PP 

oo OO o' o'o c:30 o' oo o OO OO o'o OO oo' OO oc:J oo oo 



o 



J2 

=1 

GQ 



o 

m 



w 



7T! oo 



a 



W^- 



h40 



w 
o 



o 



iz; <jj 2; Iz; cQ W 



o 



o 

w 



o d 



o 
d 



w 
o 

m 

2 



152 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

owing to the possible hydrolysis of the salt, as well as to certain reactions 
which appear to take place in the solutions at the higher temperatures." 
The ionization of hydrochloric and nitric acids falls off much more 
rapidly than does that of the salts and that of nitric acid falls off more 
rapidly than that of hydrochloric acid, as may be seen from Table LIV. 
At 0.08 normal and 306°, the ionization of nitric acid is only about one 
half that of hydrochloric acid. At that temperature the ionization of 
hydrochloric acid is approximately the same as that of the typical binary 
salts, such as potassium and sodium chlorides. The ionization of weak 
electrolytes, such as ammonium hydroxide and acetic acid, falls off much 
more rapidly than does that of the strong electrolytes. Correspondingly, 
at a given concentration, the maximum in the conductance-temperature 
curves occurs at lower temperatures in the case of weak acids and bases. 
For acetic acid this maximum lies in the neighborhood of 100°. 

The ionization of salts of higher type, as well as that of the more 
complex acids and bases, such as sulphuric acid and barium hydroxide, 
falls off very markedly with the temperature, and the decrease is as a 
rule the greater the higher the type of the salt. This is well illustrated 
in the case of magnesium sulphate, whose ionization at 0.08 normal and 
218° is only 7 per cent. Corresponding to this rapid decrease in the 
ionization of the more complex salts at the higher temperatures, the 
maximum in the conductance ciirves lies at relatively low temperatures. 

As the temperature rises, the dielectric constant of water decreases 
and we should expect the properties of aqueous solutions to approach 
those of non-aqueous solutions. This is indeed the case. At. higher tem- 
peratures, the ionization values for different electrolytes approach those 
of the same type of electrolytes in solvents of lower dielectric constants. 
The low ionization values of the salts of higher type correspond with 
the relatively low values of the ionization of the same type of salts in 
nearly all non-aqueous solvents. At 306°, many of the properties of 
electrolytic aqueous solutions, which differentiate these solutions from 
similar solutions in non-aqueous solvents, have in large measure dis- 
appeared. So, for example, the great difference in the conductance 
values of the different ions has almost completely disappeared at 306°. 
Similarly the abnormally high ionization values of hydrochloric and 
nitric acids, as well as of the strong bases, have disappeared at this 
temperature. And, finally, the ionization function, for the binary elec- 
trolytes at any rate, approaches values not very different from those of 
solutions in many non-aqueous solvents. 

It is evident that, since the ionization decreases with the temperature, 

" Noyes, loc. cit., p. 94. 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 153 

the value of the ionization function likewise decreases. It is interesting 
to examine the general course of the ionization function at different 
temperatures. In the following table are given values of the ionization 
function K' at a series of concentrations at 156° and 306°, for potassium 
chloride, and at 156°, 218° and 306° for nitric acid. 

TABLE LV. 

Values op the Ionization Function K' for Strong Electrolytes in 
Water at Higher Temperatures. 

Potassium Chloride. 

C X 10=" 0.5 2.0 10. 80. Temp. 

K'XiO^ 2.68 5.67 18.9 39.6 156° 

— 0.882 — 13.0 306° 

Nitric Acid. 

C X 10' 0.5 2.0 10. 80. Temp. 

K' X 10^ 2.68 4.87 10.7 28.0 156° 

1.57 3.53 8.30 21.6 218° 

0.60 1.22 2.96 8.53 306° 

Allowance must, of course, be made for the more or less continuous 
increase in the probable error of the conductance values as the tem- 
perature rises. The uncertainty in the value of the ionization function 
K', however, probably does not increase in the same proportion, since, 
at a given concentration the ionization of the salt decreases with tem- 
perature, and a given percentage error in A or Ao has as a consequence 
a smaller percentage error in the value of K'. At the higher concentra- 
tions, at any rate, the values of K' are approximately correct. In the 
case of potassium chloride at 156°, the general course of the curve is 
similar to that of potassium chloride at 18°, but the value of the function 
is somewhat lower. At 306°, the value of the function K' is markedly 
lower than at 156°. Thus, at 0.08 normal, between 156° and 306°, K' 
changes from 0.396 to 0.13. Correspondingly, at lower concentrations 
the value of the function K' becomes much smaller. The change in the 
value of the function K' is most marked in the case of nitric acid. For 
this electrolyte, between 156° and 306°, the value of K' decreases ap- 
proximately in the ratio of 1 to 4. For hydrochloric acid the change in 
the value of K' is much smaller than it is for nitric acid. Since, at 
306°, the ionization curve of hydrochloric acid differs but little from that 
of potassium chloride, it is obvious that the value of the function K' for 
hydrochloric acid is approximately the same as for potassium chloride 
at that temperature. At 18° and 0.1 N, the value of K' is 0.5 for potas- 



154 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

sium chloride and 1.1 for nitric acid. It is evident that at the higher 
temperatures the strong acids and bases are relatively much weaker 
than at lower temperatures. 

Owing to uncertainties in the conductance values and the meagreness 
of the experimental material at the higher temperatures, it is not possible 
to determine whether or not the mass-action law actually is approached 
as a limiting form in the case of aqueous solutions; but it seems not 
unlikely that such is the case. In view of the high value of the ioniza- 
tion constant of water and the relatively low value of the ionization 
function of the acids and bases at higher temperatures, it follows that at 
these temperatures typical salts will be hydrolyzed to an appreciable 
extent in dilute solutions and that salts of slightly weaker acids and 
bases, and particularly of the polybasic acids and the polyacid bases, 
undergo appreciable hydrolysis. 

3. The Conductance of Solutions in Non-Aqueous Solvents as a 
Function of the Temperature. In aqueous solutions, the maxima of the 
temperature-conductance curves lie at temperatures which are the lower 
the higher the concentration of the solution. The observed conductance 
change with rising temperature is the resultant effect of an increase in 
conductance due to increasing fluidity of the solvent, and a decrease, 
due to decreasing ionization of the salt. In very dilute solutions, where 
the ionization is approaching unity in all cases, the conductance in- 
creases with the temperature at all temperatures, since the ionization 
remains practically fixed in the neighborhood of unity, while the fluidity 
of the solvent increases. At higher concentrations, the ionization de- 
creases with the temperature and presumably, at sufficiently high tem- 
peratures, it decreases at a sufficient rate to overcome the increase in 
conductance due to the fluidity change of the solvent. When the two 
effects balance, the temperature coefficient becomes zero, while at higher 
concentrations the temperature coefficient becomes negative. 

In non-aqueous solutions, particularly in solvents of low dielectric 
constant, the temperature-conductance curves, as functions of the con- 
centration, have a somewhat different form. In very dilute solutions, 
where the ionization is great, the conductance increases with the tem- 
perature because of the increasing fluidity of the solvent. At certain 
intermediate concentrations and above certain temperatures, the con- 
ductance decreases with the temperature, although at much lower tem- 
peratures the curve in general passes through a maximum. At much 
higher concentrations, that is, in the neighborhood of normal and above, 
the temperature coefficient is again throughout positive; that is, the 
conductance increases with the temperature at all temperatures. In the 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 155 

following table are given values of the conductance of potassium iodide 
and ammonium sulphocyanate in SO^ at temperatures from —33° to 
+ 10° - 



">o 12 



TABLE LVI. 

Conductance of Electrolytes in SO^ at Dipfeeent Temperatures. 

Potassium Iodide. 



V 


— 33° 


— 20° 


— 10° 


0° 


+ 10° 


1.00 
128.0 
4000. 


37.7 

65.9 

139.0 


44.1 

66.9 

151.0 


46.9 

66.5 

162.5 


51.2 

64.5 

166.3 


54.5 

62.0 

168.7 




Ammonium Sulph 


ocyanate. 






1.28 
167.1 


9.42 
17.01 


10.17 
16.44 


10.82 
15.92 


11.13 
15.10 


11.33 
14.01 



It will be observed that in the neighborhood of normal the con- 
ductance curve for both salts rises throughout with increasing tempera- 
ture. In the neighborhood of 0.01 normal there is a slight increase 
between — 33° and — 20° in the case of potassium iodide, after which 
the conductance decreases throughout with the temperature. At the 
lower concentration, the conductance of ammonium sulphocyanate de- 
creases throughout with increasing temperature. At a dilution of four 
thousand liters, the conductance of potassium iodide increases throughout 
with increasing temperature. 

The effect of temperature on the conductance of solutions in non- 
aqueous solvents is readily interpreted in terms of Equation 11. What 
we have to consider is the influence of temperature upon the constants 
of this equation. We have seen that as the dielectric constant of the 
solvent decreases, i.e., as the temperature rises, the value of the constant 
K decreases and ultimately reaches very low values. On the other hand, 
as the dielectric constant decreases, the exponent m increases while the 
constant D remains practically independent of the dielectric constant of 
the solvent. If the mass-action constant K is not too small, then, at high 
dilutions, the ionization of the electrolyte will approach unity, whatever 
the dielectric constant of the solvent. It follows, therefore, that with 
increasing temperature the conductance of such dilute solutions will 
increase throughout as the temperature increases. The constant D, as 
we have seen, determines the value of the ionization at very high con- 
centrations. At unit ion concentration the value of the ionization is 

"Franklin, J. Phya. Chem. 15, 6T5 (1911). 



156 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Y = ~_ For strong electrolytes D has a value in the neighborhood 

of 0.35. The ionization at this concentration is therefore 0.26 and the 
concentration of the salt at this ion concentration is accordingly in the 
neighborhood of 4.0 normal. If the constant D is independent of tem- 
perature, then the ionization at this concentration will remain fixed and 
consequently, with increasing temperature, the conductance of the solu- 
tion will increase throughout, since the fluidity of the solution increases 
with increasing temperature. At very high and at very low concentra- 
tions, therefore, the conductance of all solutions should increase with 
increasing temperature. At intermediate concentrations, the ionization 
decreases as the dielectric constant decreases ; that is, as the temperature 
increases. The decrease in the ionization in this region is largely deter- 
mined by the decrease in the value of the constant K and increase in 
the value of the exponent m. For higher values of the dielectric con- 
stant and for salts having a high value of the constant K and low value 
of the constant D and a value of the exponent m less than 1, the change 
of the constants m and K has relatively a small effect upon the value of 
the ionization at intermediate concentrations. As a result, at low tem- 
peratures, or rather, for values of the dielectric constant greater than 
about 20, the ionization changes but little as the temperature increases 
and such solutions exhibit a positive temperature coefficient over the 
entire range of concentration. When, however, the dielectric constant 
falls below a value in the neighborhood of 20, the exponent m increases 
markedly and the constant K decreases largely with temperature. Con- 
sequently, at intermediate concentrations, the decrease in the ionization 
more than compensates for the increase in the conductance due to the 
increased fluidity of the solutions. The conductance of solutions at such 
intermediate concentrations, therefore, decreases with increasing tem- 
perature. 

In order to illustrate the effect of temperature upon the conductance 
of solutions, ionization and conductance curves have been calculated for 
an electrolyte having the constants given in the following table: 

TABLE LVII. 

Assumed Constants of Equation 11 to Illustrate the Effect of 
Temperature on Conductance. 

X X 10^ m D 

5.2 1.21 0.4 

8.5 1.14 0.4 

13.0 1.05 0.4 

20.0 0.95 0.4 



t 


Ao 


-1-10° 


240 


— 10° 


200 


— 30° 


160 


— 50° 


120 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 157 

These constants correspond very nearly with those for solutions of potas- 
sium iodide in sulphur dioxide. The data for these solutions present 
certain inconsistencies, particularly at low concentrations, which render 
it very difficult to determine the precise values of A„. Accordingly, the 
approximate constants given above have been adopted for the purpose 
of illustrating the effect of temperature upon the ionization and con- 
ductance of an electrolyte. The constant D is assumed to be inde- 
pendent of temperature. This condition is approximately fulfilled in 
solvents having dielectric constants lower than 25. The lower curves 




ao T.o 

Log V. 

Fig. 33. Illustrating the Influence of Temperature on the Ionization and the Con- 
ductance of Electrolytes in Solvents of Relatively Low Dielectric Constant. 

in Figure 33 represent the values of the ionization at different tempera- 
tures, the lower curves corresponding to the higher temperatures. In 
order to secure a plot on which the ionization and conductance values 
may be conveniently represented at all concentrations, the logarithms of 
the concentrations, instead of the concentrations themselves, have been 
plotted as abscissas. It will be observed that the ionization curves inter- 
sect at a concentration of 3.6 normal, corresponding to the value log 
C = 0.556. Actually, the intersections do not occur at a point, since the 

D -4- K 

and the constant K 



ionization is given by the equation y '■ 



l+D^K 



158 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

decreases slightly as the temperature increases. The value of K, how- 
ever, is so small that this effect is scarcely appreciable. At concentra- 
tions greater than 3.6 normal, the ionization increases with the tempera- 
ture, and this increase is the greater the greater the value of m. In 
general, the increased conductance due to increased ionization in these 
regions is masked by the rapidly increasing effects of viscosity. In the 
neighborhood of normal concentration the viscosity effect becomes suffi- 
ciently great to overbalance the conductance increase due to increased 
ionization and the conductance-temperature curves pass through a maxi- 
mum in this region, after which they fall off very rapidly. Nevertheless, 
it is to be noted that, in all cases for which measurements are available 
at different temperatures in very concentrated solutions, the conductance 
increases markedly with the temperature and this increase is the greater 
the higher the concentration. In Table LVIII are given values of the 
conductance of concentrated solutions of different salts in methylamine 
and ethylamine at a series of temperatures." 

What is striking in these results is the high value of the temperature 
coefficient at high concentration, as, for example, in solutions of silver 
nitrate in methylamine at V = 0.2456. Between — 33.5° and — 15° 
the conductance increases 91 per cent or 4.92 per cent per degree. The 
same holds true for solutions of silver nitrate in ethylamine, where the 
conductance increases nearly 100 per cent between — 33.5° and — 15° 
at 0.4083 N, while, between ■ — 15° and 0°, the conductance of solutions 
of ethylammonium chloride increases 6.76 per cent per degree at 0.17 N. 
It is true that the viscosity in these concentrated solutions must differ 
greatly from that of the solvent and the viscosity may change much 
more rapidly with the temperature in the case of the concentrated solu- 
tions than in that of the more dilute solutions. Nevertheless, it appears 
not improbable that the high value of the temperature coefficients of 
concentrated solutions is in part due to the increased ionization at these 
high concentrations. 

As the concentration decreases below 3.6 N, the ionization decreases 
with increasing 1«mperature. Those solutions for which m is less than 
unity exhibit an increase in ionization throughout with decreasing con- 
centration, while those solutions for which m is greater than unity exhibit 
first a decrease and then an increase, so that the ionization curves pass 
through minima in the neighborhood of 0.1 N. These minima are the 
more pronounced the greater the value of m. In very dilute solutions 
again, the ionization curves approach one another, corresponding to the 
fact that at low concentrations the ionization in all cases approaches unity. 

"Fitzgerald, J. Phye. Chem. 16, 621 (1912). 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 159 

TABLE LVIII. 

Conductance of Concentrated Solutions in Methylamine and 

Ethylamine. 







MethylamiiM 


^ 






Salt 


V 


— 33.5° 


— 15° 


0° 


+ 15° 


AgNOs 


. 0.2456 


3.237 


6.180 


9.262 


13.05 


it 


. 0.4790 


14.33 


20.56 


25.67 


30.8 


it 


. 0.9348 


22.61 


28.92 


34.15 


38.77 


(( 


. 2.084 


24.32 


29.48 


32.97 


34.95 


" 


. 5.449 


21.80 


25.18 


26.81 


27.41 


(( 


. 10.63 


20.04 


22.19 


22.74 


22.19 


KI 


. 0.6094 


31.12 


38.17 


42.90 


46.49 


li 


. 1.190 
. 2.320 


32.97 
28.49 

Ethylamine 


38.52 
31.45 


41.74 
33.90 


43.96 


it 


33.39 






AgNOe 


. 0.4083 


2.135 


3.989 


5.824 


8.072 


il 


. 0.7968 


5.310 


7.753 


10.09 


12.11 


11 


0.9928 


5.67 


8.44 


10.55 


12.52 


11 


. 1.981 


5.820 


7.625 


9.082 


10.25 


It 


. 3.953 


4.320 


5.400 


6.141 


6.719 


(1 


. 7.886 


2.683 


3.181 


3.454 


3.690 


(( 


. 15.73 


1.677 


1.818 


1.939 


1.939 


11 


. 31.39 


1.212 


1.277 


1.285 


1.188 


LiCl 


. 0.4215 





— 


1.586 


2.080 


li 


. . 0.8224 
. 1.604 
. 3.131 

. 0.1666 


1.279 
0.8484 


2.001 
1.763 
0.9915 

0.7197 


2.447 
1.911 
0.976 

1.450 


2.661 


K 


1.835 


<( 


0.8052 


C^H^NHsCl ... 


2.440 




. 0.3253 


2.293 


3.851 


5.242 


6.616 


(( 


. 0.6346 


— . 


5.090 


5.820 


6.406 




. 0.7676 


3.692 


4.675 


5.294 


5.630 


(I 


. 1.497 


2.606 


2.921 


2.992 


2.886 




. 2.922 


1.285 


1.261 


1.181 


1.064 



If the values of the ionization given by the lower curves in the figure 
are multiplied by the corresponding Ao values, the conductance curves 
shown in the upper part of the figure are obtained. At low concen- 
trations, where the ionization decreases only little with rising tempera- 
ture, the increased conductance, due to temperature rise, more than 
counterbalances the decreased conductance due to decreased ionization, 
and the conductance therefore increases with increasing temperature. In 
very concentrated solutions, also, the conductance increases with the 
temperature since the change in ionization here is relatively small. At 



160 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



intermediate concentrations, however, where the change in ionization is 
large, the conductance-concentration curves at different temperatures 
intersect one another in a more or less complicated manner, indicating 
that the conductance-temperature curves in this region exhibit maxima. 







— 1 1 ■ - 




























































/ 






/ 






/ 


100 


/ 


t 

/ 

/ 


, «»' 




f 






< ^' 


^^ 


/ 


<a 


^y^ 


/ 
/ 


o 




/ 


S oo*' 


"^ 


/ 

/ 


2 ««•" 




/ 


T3 




/ 


g 




/ 


^ ...0. 


-^ 


/ 
/ 


a 




/ _ 


Ol 






■« SO 




/ — — _ 




- — 


» — -*"-'^^^ 


--^^;::::= 


s=^^ — — _ 


<:..»' 


.-■ — 




c- to 




1 ' 



C'.ooi 



- lOO 



C'.0O5| 



- so 



Cx 


■ 01 


c« 


(■0 


C t 


•31 
•0»l 

O.I 



'SO 



-30 ~IO 

Temperature. 



*IO 



Fig. 34. Conduotance-temperature Curves, illustrating the Relation between Con- 
ductance and Temperature for Solutions of Electrolytes at Different Concentra- 
tions in Solvents of Relatively Low Dielectric Constant. 

The temperature-conductance curves are shown in Figure 34 for concen- 
trations from 1.0 to 0.001 normal. At 0.001 normal the conductance 
increases throughout with increasing temperature. As the temperature 
rises, however, the conductance change due to a given temperature change 
becomes smaller and smaller and at this concentration the curve is very 
near a maximum at a temperature of -|- 10". At a concentration of 
0.0031 normal, the conductance curve exhibits a very flat maximum at a 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 161 

temperature of — 10°. As the concentration of the solution increases, 
the maximum is shifted toward lower temperatures as indicated by the 
dotted curve. At 0.01 normal the maximum lies in the neighborhood of 
— 30°, while at 0.031 normal the maximum is still further displaced in 
the same direction. At 0.1 normal the maximum remains at practically 
the same value, but at 0.31 normal the maximum is displaced toward 
higher temperatures, being very flat in this case and lying somewhere 
in the neighborhood of — 10°. At 1 normal the maximum has arisen to 
temperatures above + 10° and the conductance increases markedly over 
the entire temperature range from —50° to +10°. The maximum 
occurs at the lowest temperature at a concentration in the neighborhood 
of 0.1 N. These curves represent, in general, the behavior of solutions 
at different temperatures. They correspond very closely with the values 
obtained by Franklin " for solutions of KI in SO^. The maximum in 
the conductance-temperature curves shifts from higher to lower tem- 
peratures with increasing concentrations, reaches a minimum, and there- 
after again shifts from lower to higher temperatures with increasing con- 
centration. In certain cases the effect of viscosity is such that it just 
counterbalances the effect of increased ionization over a considerable 
temperature interval. Ammonium sulphocyanate dissolved in sulphur 
dioxide is an example of this type, the conductance being practically 
independent of temperature at a concentration of approximately 0.1 
normal. At concentrations greater than 0.1 normal the temperature 
coefficient of ammonium sulphocyanate solutions in sulphur dioxide is 
positive and is the greater the greater the concentration of the solution, 
while at lower concentrations the temperature coefficient is negative and 
initially increases with decreasing concentration. Ultimately, however, 
the sign of the coefficient must change. The fact that solutions in all 
solvents, without exception, exhibit maxima in the conductance-tempera- 
ture curves at intermediate concentrations indicates that at the tem- 
peratures in question the constant m has reached a value near or 
greater than unity. Curves of this type have been observed in solu- 
tions in ammonia, sulphur dioxide, water, methyl and ethyl amine, and 
methyl and ethyl alcohols. It is not to be doubted that the phenomenon 
is a general one. That the temperature coefficient of solutions becomes 
positive at very high concentrations is indicated by practically all data 
available for solutions at high concentrations. In general, it has been 
found that the higher the concentration the greater the value of the tem- 
perature coefficient, or rather that the temperature coefficient passes 
through a minimum or negative value at intermediate concentrations. 

" Franklin, loc. cit. 



162 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



This result, however, does not become apparent in solutions of high 
dielectric constant, since the effects in question become marked only 
when the constant m approaches a value of unity or greater. 

With increasing concentration, the temperature of the conductance 
maximum decreases, passes through a minimum and thereafter again 
increases in the more concentrated solutions. This course of the curve 



■6*55. 




V'saz.-, 



»' = i6l.. 



V = 80.7 

V = 6S.14 

V =• 32.6 

V = I6.3 

V-S.(7 



Temperature. 

Fig. 35. Showing the Conductance as a Function of the Temperature for Solutions 
ot Lobalt Chloride m Ethyl Alcohol at Different Concentrations. 

is illustrated in Figure 35, in which are plotted the temperature-con- 
ductance curves for cobalt chloride, CoCl^, in ethyl alcohol." The 
course of the maximum is here indicated by the broken line. The lowest 
point of the maximum temperature is approximately 31° and at a dilution 

"Bitnbach and WeitzeJ, Ztschr. /. phys. C'hem. 79, 279 (1918), 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 163 

of approximately 50 liters. At higher concentrations the maximum tem- 
perature mcreases very rapidly, while at lower concentrations the maxi- 
mum mcreases more slowly. In solvents of lower dielectric constant, 
the curve of maxima proceeds to lower temperatures. In Figure 36 are 
shown curves for cobalt chloride in acetone." In this case the branch 



\^s|S7 




Temperature. 

Fig. 36. Showing the Conductance as a Function of the Temperature for Solutions 
of Cobalt Chloride in Acetone at Different Concentrations. 

of the maximum at lower concentrations lies at very low values of the 
concentration and does not appear on the figure. At higher concentra- 
tions the course of the maximum temperature is indicated by the broken 
line. At all points to the right of the maximum curve the temperature 
coefficients of the solution are negative. In Figure 37 are shown the 
conductance temperature curves for potassium iodide in methylamine, the 
dotted curves relating to dilutions greater than 28.3 liters." The relation 

" Rlmbach and Weitzel, loc. cif. 
" Fitzgerald, Iqc. cif. 



164 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

among the curves in this case appears quite complex, since at the highest 
concentrations the conductance decreases with increasing concentration. 



eo 





-33* -I5« 

Temperature. 



+ 15" 



Fig. 37. Representing the Conductance as a Function of the Temperature for Solu- 
tions of Potassium Iodide in Methylamine at Different Concentrations. 

The course of the maximum temperatures is indicated by the broken 
lines which meet at a point at a temperature of — 33° and at a dilution 
of 28.2 liters. At higher concentrations the maximum proceeds to higher 
temperatures quite rapidly, while at lower concentrations the temperature 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 165 

of the maximum increases slowly. Similar curves have been found for 
solutions in ethylamine, methylamine, and sulphur dioxide. 

While the complete conductance-temperature diagram is not known 
for most solvents, sufficient data exist to indicate that it is a general 
property of electrolytic solutions to exhibit an increasing positive tem- 
perature coefficient at high concentrations. In certain cases this coeffi- 
cient may be very great. In other cases the coefficient at lower concen- 
trations is negative, decreasing with the concentration and becoming 
positive at higher concentrations. In the following table is given a list 
of temperature coefficients for substances dissolved in the liquid halogen 
acids.^* The coefficients are positive unless otherwise indicated. 

TABLE LIX. 

Temperature Coefficient a X 100 of Solutions of Electrolytes in 

Different Solvents. 

Hydrogen Bromide. 

Electrolyte V^ a^ V^ a^ Vg a. 

Acetic Acid 4.30 2.62 0.571 2.72 

Butyric Acid 4.18 2.68 0.817 3.70 

Iso-valeric Acid 4.37 2.45 0.729 3.96 

Benzoic Acid 8.82 0.53 2.38 0.72 1.14 0.89 

Metatoluic Acid 5.85 0.15 1.83 0.93 

Hydroxybenzoic Acid ... 18.4 1.00 1.36 2.15 

Methyl Alcohol 1.75 2.5 1.25 4.2 

Metacresol 15.0 — 7.71 1.00 + 1.16 

Thymol 43.6 .47 7.34 0.00 

Alphanaphthol 51.6 2.26 18.0 0.30 

Hydrogen Chloride. 

Propionic Acid 11.8 2.15 2.5 2.91 

Butyric Acid 50.1 2.80 0.792 3.27 

Methyl Alcohol 2.91 1.21 1.06 2.68 

Ethyl Alcohol 4.66 3.9 0.591 4.0 

Butvl Alcohol 5.07 5.23 0.574 6.5 

Resoictn . .:: 137.0-1.33 6.29 0.00 0.539+1.3 

With the exception of solutions of thymol and alphanaphthol in 
liquid hydrogen bromide, the positive temperature coefficients through- 
out increase with increasing concentration. For lack of more compre- 
hensive experimental data regarding the temperature coefficient of the 
substances named, it is impossible to hazard a guess as to the reason for 
the decrease of the positive temperature coefficients in the case of the 
solutions of these two substances. Particularly notable is the high nega- 

w Archibald, Journal de Chimie Physique U, 741 (1913). 



166 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tive temperature coefficient of the solution of metacresol in liquid hydro- 
gen bromide at a dilution of 15 liters. Evidently, the temperature 
coefficient in this case changes greatly with the concentration since at 
normal concentration the coefficient is positive and equal to 1.16 per cent. 

It is difficult to account for the large value of the positive tempera- 
ture coefficients of the very concentrated solutions, except on the assump- 
tion that the ionization in the case of these solutions is relatively inde- 
pendent of the temperature. While the concentration at which this con- 
dition is fulfilled varies considerably with the nature of the dissolved 
electrolyte, it varies but little with the nature of the solvent. While at 
lower concentrations the ionization decreases throughout with the tem- 
perature, at higher concentrations the ionization increases with the 
temperature. 

It is probable that, at very low concentrations, the temperature 
coefficient will always be found positive. The concentration at which 
this holds, however, may be very low indeed in the case of solvents of 
very low dielectric constant. It may be noted, in this connection, that 
the conductance-temperature coefficient of nearly all solvents is positive. 
It is true that, if no impurities were present, it might be expected that 
the ionization of the solvent would increase with the temperature. How- 
ever, in most cases, the final conductance of highly purified solvents is 
due to impurities and not to the ionization of the pure solvent. What- 
ever these impurities may be, it is evident that they must be sufficiently 
ionized at these concentrations to yield a positive conductance-tempera- 
ture coefficient. 

The ionization as a function of the concentration at different tem- 
peratures is represented by a family of curves passing through two com- 
mon points at a concentration zero, where the ionization is unity, and at 

a concentration corresponding to the ionization Y=^i — \ — tt, which for 

solutions of potassium iodide in sulphur dioxide is in the neighborhood 
of 3.5 normal. At concentrations below this value the ionization de- 
creases with the temperature. In very concentrated and very dilute 
solutions, the decrease in the ionization is comparatively small, and the 
conductance therefore increases with the temperature. At intermediate 
concentrations, the conductance at higher temperatures decreases with 
the temperature, while at low temperatures it increases with the tempera- 
ture. If the A, T-curves are examined, it will be found that at inter- 
mediate concentrations the conductance curves exhibit a maximum. As 
the concentration decreases, however, this maximum is displaced toward 
higher temperatures and presumably would ultimately disappear at suf- 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 167 

ficiently low concentrations. It is to be borne in mind, however, that at 
very high temperatures the value of the mass-action constant becomes 
extremely low, as may be seen from the value of this constant in the case 
of solvents having low dielectric constants. It is possible, therefore, 
that, in the case of solvents having relatively low dielectric constants, the 
mass-action constant has such a low value that a maximum in the con- 
ductance curves will not be observed in dilute solutions. At higher con- 
centrations, again, the maximum is displaced toward higher temperatures 
and if it were possible to work with solutions of sufficiently high concen- 
trations the maximum should disappear entirely. Data are not available 
in this case at temperatures approaching the critical point, but, in solu- 
tions in sulphur dioxide and ethyl amine, the conductivity increases with 
the temperature over those ranges of temperature for which conductance 
data exist. 

The conductance of a given solution, therefore, appears to be a func- 
tion, primarily, of the fluidity of the medium and of its dielectric con- 
stant. For a given type of salt the conductance curve in two solvents at 
different temperatures will be similar, provided that the two solvents 
have the same value of the dielectric constant. 

4. The Conductance of Solutions in the Neighborhood of the Critical 
Point. Data relative to the ionization of solutions in the critical region 
are entirely lacking, for which reason it is not possible to interpret the 
results of conductance measurements with any degree of certainty. How- 
ever, the conductance data indicate that the properties of solutions in 
the critical region do not differ materially from those of solutions at lower 
temperatures. Moreover, it appears that the property of forming elec- 
trolytic solutions is by no means confined to the liquid state of matter. 
Fluids above the critical point yield electrolytic solutions and even the 
solvent vapors themselves, below the critical point, possess the power of 
dissolving electrolytes, forming solutions which conduct the current. 

It has already been pointed out that, as the critical point is ap- 
proached, the conductance of solutions in solvents of low dielectric con- 
stant approaches a very low value, and that the conductance-temperature 
curve if extrapolated would intersect the temperature axis at a tem- 
perature not far removed from the critical temperature. It is known, 
however, that, once the critical point has been reached, the conductance 
falls only very slowly with increasing temperature. It other words, the 
conductance-temperature curves exhibit a discontinuity in the immediate 
neighborhood of the critical point. As will be seen below, this behavior 
is what we should expect when conductance measurements are carried 
out in sealed tubes, where the total volume of liquid and vapor remains 



168 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

constant. In the immediate neighborhood of the critical point, the 
density of the solvent decreases very rapidly with increasing temperature, 
whereas beyond the critical region the density of the solvent medium 
remains fixed. The rapid decrease in conductance immediately below 
the critical point is to be ascribed to the rapid decrease in the density of 
the solvent medium. 

It is to be expected that the ionization and consequently the con- 
ductance of solutions in the critical region will be governed largely by 
the dielectric constant of the medium, and it may be inferred that those 
liquids, which under ordinary conditions exhibit a very high dielectric 
constant, will likewise exhibit a relatively high dielectric constant in the 
critical region. In the case of sulphur dioxide and ammonia the dielec- 
tric constant in the critical region is very low, whereas in the case of the 
lower alcohols and water a relatively larger value of this constant is to 
be expected. Water would be an ideal substance for the purpose of 
studying the properties of electrolytic solutions in the critical region, 
were it not for the difficulties attending conductance measurements in 
this solvent at high temperatures. These difficulties, however, disappear 
very largely in the case of the lower alcohols, although it is to be ex- 
pected that the ionization in the critical region will be markedly lower 
in these solvents than in water. 

In Table LX are given values of the specific conductance of solutions 
of potassium iodide in methyl alcohol at a series of temperatures up to 
2520.19 The critical -point lies in the neighborhood of 240° C. The 
reduced conductance values given in the last column are derived by 
multiplying the specific conductance (second column) by the fraction 
of the total volume of the tube occupied by the liquid (third column). 
If the true critical phenomenon is to be observed, the tube must initially 
be filled with an amount of liquid such that when the critical point is 
reached the tube is just filled with liquid. Obviously, as the liquid 
expands, the concentration of the solution decreases, and the corrected 
values of the specific conductance therefore represent values of this 
quantity on the assumption that the specific conductance varies as a 
linear function of the concentration. This condition is probably not 
fulfilled, but nevertheless represents an approximation somewhat nearer 
the truth than the measured values of the specific conductance. More- 
over, in the immediate neighborhood of the critical region, where the 
volume of the liquid is almost equal to the entire volume of the tube, the 
corrected value of the specific conductance corresponds very nearly with 
the true value. If these corrected values are plotted against the tem- 

"Kraus, Pliva. Rev. 18, 40 and 89 (1904). 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 169 



perature, then a break in the conductance curve itself will not occur at 
the critical point. The results are shown graphically in Figure 38. 

TABLE LX. 

Specific Conductance of KI in CH3OH thbough the 
Ceitical Region, at 3.34 X lO"* N. 

Liquid. 



t 


nxio" 


V /V 


ViV /VX 10' 


90.0 


908.4 


0.4324 


392.8 


102.0 


1006.0 


.4363 


438.9 


123.0 


1098.0 


.4451 


488.2 


138.2 


1126.0 


.4548 


511.9 


149.0 


1139.0 


.4674 


532.3 


159.0 


1126.0 


.4764 


536.2 


171.0 


1076.0 


.4853 


522.5 


183.8 


1006.0 


.4979 


500.9 


197.0 


740.4 


.5095 


377.3 


208.5 


617.0 


.5137 


314.3 


220.0 


431.2 


.5445 


234.8 


225.0 


337.5 


.5569 


187.9 


230.0 


252.1 


.5693 


143.5 


237.0 


186.0 


.6005 


in.6 


238.0 


157.6 


.6094 


96.05 


238.5 


143.7 


.6183 


88.88 


239.0 


127.0 


.6275 


79.69 


239.5 


107.5 


.6362 


68.39 


240.04 


83.71 


.6628 


55.50 


240.4 


63.92 


.7432 


47.50 


240.5 


55.46 


.8074 


44.78 


240.6 


45.29 


.9566 


43.32 


Crit. 


42.65 

Gas. 


1.000 


42.65 


t 


jxXlO" 


t 


fiXlO" 


240.7 


42.14 


242.45 


36.10 


240.8 


41.56 


243.4 


34.45 


240.9 


40.98 


244.4 


32.88 


241.0 


40.41 


245.46 


31.24 


241.2 


39.52 


247.1 


29.11 


241.4 


38.68 


249.1 


26.59 


241.6 


37.89 


252.0 


23.92 


241.92 


37.06 







It will be observed that the conductance passes through a maximum 
somewhere between 159° and 197°, probably not far from 175°. There- 
after the conductance decreases rapidly, particularly in the immediate 



170 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

neighborhood of the critical point, which in this case is 240.6°. At the 
critical point the rapid decrease in conductance with the temperature 
ceases abruptly and thereafter there is only a moderate decrease as the 
temperature increases. Between 239.5° and 240.6° there is a conduct- 
ance decrease of approximately 50 per cent for a temperature change of 
1°, whereas between 240.6° and 252° there is a decrease of less than 
50 per cent for a temperature change of approximately 12°. The sharp 
break in the tangent to the curve at the critical point is very noticeable. 



3 

a 
o 
O 



rt 




/zo' I'fo' 160' (BO' ZOO' zeo' ^t^o• 

Temperature. 

Fig. 38. Representing the Conductance of Solutions of Potassium Iodide in Methyl 
Alcohol as a Function of the Temperature through the Critical Region. 



This result is obviously due to the fact that below the critical temperature 
the observed conductance change is due to the combined effect of tem- 
perature and of density change, while above the critical point it is due 
to temperature change alone. 

As the critical point is approached, the salt becomes appreciably 
soluble in the vapor and is sufficiently ionized to render the vapor a 
fairly good conductor. In Table LXI, are given values of the specific 
conductance of liquid and vapor for solutions of ammonium chloride in 
methyl alcohol, together with the relative volume of the liquid 

phase 



t 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 171 



In this solution the amount of liquid in the tube was such that its 
mean density was below the critical density. In such case the true 
critical phenomenon does not occur since, if carried out under strictly 
equilibrium conditions, the liquid disappears at the bottom of the tube. 
In general, however, unless the amount of liquid is comparatively small, 

TABLE LXI. 

Conductance of 0.2245 Per Ceni NH^Cl in CH3OH in the 
Critical Region. 

Temp. [X Liquid u, Vapor F./F 

234.0 1524.0 .4411 

236.9 1236.0 1.574 .4333 

239.0 930.3 2.177 .4261 

240.0 760.0 3.568 .4147 

241.0 605.7 6.381 .4000 
241.9 469.7 14.64 .3707 
242.5 257.7 38.66 .2806 

-^ Crit. Pt. 

243.1 67.25 

245.2 54.36 
247.1 47.62 
249.0 41.33 
254.0 30.19 

and is thoroughly stirred, it will be found that the meniscus fades away 
at some point above the bottom of the tube at a temperature correspond- 
ing to the critical temperature. At this temperature, the specific con- 
ductance of the vapor phase was approximately one sixth that of the 
liquid phase. The conductance of the vapor phase is readily appreciable 
as much as 5° below the critical point. Above the critical point the 
conductance of the solution in a gas below its critical density decreases 
with the temperature, the decrease amounting to something over 50 per 
cent for a temperature change of approximately 12°. In the immediate 
neighborhood of the critical point the conductance appears to change 
somewhat more rapidly than at higher temperatures. 

The conductance of the vapor phase increases very rapidly with the 
temperature, and the more rapidly the nearer the temperature lies to the 
critical point. It is evident that several factors are here coming into 
play. In the first place, the concentration of the salt in the vapor phase 
increases with rising temperature; and, in the second place, the density 
of the vapor increases with increasing temperature. As follows from 
the results given below for the conductance of the fluid phase above the 
critical temperature as a function of the concentration of the solvent, the 



172 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

conductance increases very rapidly with increasing density of the solvent 
phase. As the density of the vapor increases as the critical point is 
approached, the conductance is increased very largely because of the 
increase in the density of the vapor. The relations between the curves 
are shown in Figure 39. 

In the following table are given values of the specific conductance 
of a 0.00463 normal solution of potassium iodide in methyl alcohol for 
different concentrations of the solvent.^" 

TABLE LXII. 

Conductance of Potassium Iodide in Methyl Alcohol above the 
Critical Point for Different Densities op Solvent. 



c = 


0.1188% 


V = 0.3981 


W = 0.1163 


C = { 


3.00463 N 








V 


iX10« 






W-- 


= 0.1163 


0.1023 


0.0968 


0.0815 


0.0758 


0.0588 


239.0 


— 


— 


— 


— 


— 


1.892 


241.0 


— 


— 


— 


— 


— 


1.736 


241.3 


— 


— 


— 


— 


4.783 





241.32 


— 


42.24 


— 


— 








241.5 


56.41 


. — . 


— 











241.6 


— 


— 


28.80 


— 








241.7 


— 


. — . 


— 


16.56 








242.0 


53.95 


36.35 


26.54 


10.90 


4.468 





242.9 


— 


— 


— 


— 





1.662 


243.0 


50.54 


32.48 


24.23 


9.36 


4.141 





244.0 


47.90 


30.59 


22.47 


8.626 


3.884 





244.9 


— 


— 


— 


— 




1.521 


245.0 


— 


28.80 


21.25 


7.886 


3.656 




245.1 


45.51 


— 


. — . 


. 







247.0 


41.68 


25.79 


19.14 


7.081 


3.247 




247.2 


— 


— 


— 


— 




1.387 


250.1 


36.97 


22.04 


16.90 


6.003 


2.824 


1.230 



In this table W represents the weight of solvent in the tube, V the 
total volume of the tube in cubic centimeters and C the concentration of 
the solution. The conductance curves are shown graphically in Figure 
40. The density of the solvent in the different experiments, together with 
he conductance of the solutions at 245° and 250°, is given in Table 
LXIII. (See page 174.) 

It is evident that the conductance of a solution containing a given 
amount of salt and a variable amount of solvent increases enormously 
as the density of the solvent increases. For an increase in the density 
of the methyl alcohol from 0.127 to 0.251, the conductance increases 



"> Kraus, loc. cit. 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 
600 



173 




240" 2+a' 244° 

Temperature °C. 



2S0° 



Fig. 39. Representing the Conductance of Ammonium Chloride in Methyl Alcohol 
as a Function of the Temperature in the Critical Region. 



fiO 
























































"~" 




~~ 


~~ 








— 




- 


— 




















ir 


















































- 


- 


- 
















■J 
































































s 












































50 






























S 










































































V 












































































> 
























































































































































'~- 


■«., 
























40 


















































" 
















































































~~ 


^ 












UJ 

> 

O 
=) 
o 
z 
o 
o 
































































■^ 
































N 








































































s 


«, 








































30 
































^ 


>f 
























































-s 














■" 




■^ 






















































S| 




















■- 





















































<.^ 


^ 


























^ 


















































1> 
























■^ 


— 










20 
























































































































-^ 






__ 












































































^~ 


^ 




-f 






















































































































































10 
























-f 










































































'*" 








-1- 


















































































— 


— 


' — 


- 




, 






































* 


— 


+ 


_ 




































, 




















































— 


— 


— 






— 


r— 


— 


^ 




^ 














1 


























■^ 


— 








— 


— 


— 






— 




~~ 


1 











237 



23» 



241 



243 245 

TEMPERATURES 



247 



24» 



25) 



FiQ. 40. Representing the Conductance of Potassium Iodide in Methyl Alcohol 
' above the Critical Point at Various Concentrations of the Solvent. 



174 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE LXIII. 

Conductance of KI in CH3OH as a Function of the Density 
OF THE Solvent. 



Density 


jiXlO^ 


of Solvent 


245° 250° 


0.251 


45.6 37.2 


0.220 


28.8 22.6 


0.208 


21.2 16.83 


0.178 


8.0 6.0 


0.163 


3.7 2.8 


0.127 


1.44 1.2 



from 1.44 to 45.6, or approximately 50 times. At 250° the increase in 
the conductance is not so great, since for the same concentration change 
the conductance increases only from 1.2 to 37.2, or 30 times. The 
A, i-curves indicate a fairly rapid decrease in the conductance immedi- 
ately above the critical temperature. As the temperature rises these 
curves appear to approach a horizontal straight line. The lower the 
concentration, the less does the conductance change with the temperature. 

At a given temperature, the addition of a given amount of solvent 
increases the conductance the more the greater the density of the solvent. 
In other words, the A,C-curves at constant temperature are strongly 
convex toward the axis of concentrations. 

It is to be borne in mind that the conductance of a solution is a 
function of the number of carriers and the speed with which these car- 
riers move. Unless the nature of the carriers changes very greatly, we 
should expect that the speed of the carriers would be the greater the 
lower the density of the solvent, since the viscosity of a gas increases 
with its density. Since, now, the conductance of a solution increases 
very rapidly with the density and since this increase is the greater the 
greater the density of the solvent, it is difficult to escape the conclusion 
that the increase in the conductance of these solutions is due to an 
increase in the number of carriers present in them. 

According to the commonly accepted theory of electrolytic solutions, 
the change in the conductance of solutions as a function of the concent 
tration is due to a change in the relative number of carriers; that is, 
to a change in the ionization of the electrolyte. Because of various 
difficulties which have arisen in accounting for the properties of strong 
electrolytes, some writers have suggested that strong electrolytes in 
solution are completely ionized. The study of the properties of non- 
aqueous solutions and of solutions at higher temperatures yields no 
apparent support for such an hypothesis, If the salts in solvents of low 



SOLUTIONS AS A FUNCTION OF TEMPERATURE 175 

dielectric constant are completely ionized, then it becomes exceedingly 
difficult to account, on the one hand, for the very low value of the con- 
ductance of these solutions at certain intermediate and low concentra- 
tions and, on the other hand, for the very rapid increase in the conduct- 
ance of these solutions at higher concentrations. So, in the case of 
solutions in the neighborhood of the critical point, it is difficult to account 
for the rapid decrease in the conductance of the solution as the critical 
point is approached on the basis of this hypothesis. Again, in the case 
of solutions above the critical point, the large increase in the conductance 
of the solution as the concentration of the solvent increases is with diffi- 
culty accounted for on the assumption that the electrolyte is completely 
ionized, unless, at the same time, an hypothesis is introduced according 
to which the speed of the ions through the solvent medium is enormously 
increased by an increase in the concentration of the solvent. For such 
an hypothesis there is an entire lack both of experimental facts and of 
theoretical support. 

On the other hand, if the fundamental elements of the usual theory 
of electrolytes are accepted, we are forced to the conclusion that the ion- 
ization of electrolytes is a complex function of the concentration and that, 
at very high concentrations, in the case of solvents of low dielectric con- 
stant, the ionization increases with the concentration. While theoretical 
support is lacking for this assumption, no theoretical principles are con- 
tradicted by such an hypothesis. Furthermore, if we assume that the 
ionization of electrolytes is a function of the concentration and is approxi- 
mately measured by the conductance ratio -r-, the influence of tempera- 

ture, of concentration, and of the viscosity of the solvent may be readily 
accounted for without contradicting known facts and without intro- 
ducing any further hypotheses for which a theoretical foundation is 
lacking. In other words, on the basis of the ionization hypothesis, it is 
necessary to make only a single assumption whose correctness remains 
uncertain, whereas in the case of other hypotheses a number of assump- 
tions are necessary. Unless other and more conclusive facts can be 
adduced in support of the hypothesis that the strong electrolytes are 
completely ionized in solution, this hypothesis is clearly untenable at 
the present time. 



Chapter VII. 
The Conductance of Electrolytes in Mixed Solvents. 

1. Factors Governing the Conductance of Electrolytes in Mixed 
Solvents. Since the properties of electrolytic solutions are functions of 
the properties of the solvent, it follows that in the case of mixed solvents 
the properties will be functions of the concentration of the solvents in the 
mixture. We may have mixtures in which either one or both of the 
solvents are capable of forming electrolytic solutions with ordinary salts. 
In the case of water, mixtures are, as a rule, obtained only with other 
solvents which have the power of forming electrolytic solutions. In the 
case of certain non-aqueous solvents, however, mixtures may be obtained 
with solvents not capable of forming electrolytic solutions with ordi- 
nary salts. 

The addition of a second solvent component to a solution of given 
concentration will in general affect the conductance in that the speed 
of the ions and the ionization of the electrolyte will be influenced by the 
addition of the second solvent. The conductance will therefore be a 
more or less complex function of the relative concentration of the two 
solvents. The effect of the addition of a second solvent will depend 
upon the concentration of the electrolyte as well as upon its nature. 

In certain solutions, the formation of an electrolytic solution depends 
upon an interaction between the dissolved substance and the solvent. 
When such is the case, the conductance of the solution is often greatly 
affected by the addition of a second solvent component. Such is the case 
with solutions of the acids in non-aqueous solvents on the addition of 
water. The addition of a small amount of water to a solution of an 
acid in an alcohol, for example, has an enormous influence upon the 
properties of the resulting solution. Similar results are obtained in non- 
aqueous solutions of salts which exhibit a pronounced tendency to form 
hydrates, as, for example, calcium chloride. 

If we assume that the nature of the ions remains fixed and inde- 
pendent of the nature of the second solvent, then we should expect the 
speed of the ions to be a function of the viscosity of the medium. The 
viscosity of a mixture of two solvents varies continuously with the rela- 
tive concentration of the solvents. The viscosity curves may exhibit 
either a minimum or a maximum or they may vary continuously between 

176 



ELECTROLYTES IN MIXED SOLVENTS 177 

the values of the two pure media as extremes. If the viscosity of the two 
solvents differs greatly, then in general the viscosity of a mixture will lie 
intermediate between that of the two pure components. If the two sol- 
vents have approximately the same viscosity and particularly if both 
solvents are associated liquids, the viscosity curve will as a rule exhibit 
a maximum. Cases in which the viscosity curve passes through a mini- 
mum are rather exceptional. 

The viscosity of a mixture of two solvents will in all cases be of the 
same order of magnitude as that of the two components. If the nature 
of the ions remains fixed, therefore, the speed of the ions may be ex- 
pected to vary approximately in proportion to the fluidity change. 

In adding a second solvent to a solution of an electrolyte in another 
solvent, an interaction may take place between the electrolyte and the 
added solvent. In this case, the nature of the ions will change and with 
it, in general, their speed. In some instances, the change in the speed 
of the ions due to this cause is relatively large. 

In general, it may be expected that the ionization of a salt in a mixture 
of two solvents, particularly in dilute solutions, will have a value inter- 
mediate between those of the same electrolyte in the pure solvents. For 
we have seen that the ionization of a salt is a function of the dielectric 
constant of the medium, and the dielectric constant of a mixture of two 
solvents is in general intermediate between those of the pure components. 
Here again, however, we have to take into account the interaction between 
the electrolyte and the components which form the solvent medium. If 
interaction takes place between the second solvent and the electrolyte, 
then a new complex is formed whose ionization may differ greatly from 
that of the same electrolyte in the first solvent and, in fact, all of whose 
chemical properties may differ greatly from those of the original electro- 
lyte in the first solvent. A considerable number of examples of this type 
are found in aqueous solutions. When, for example, ammonia is added 
to a solution of a silver salt in water, a complex is formed between the 
silVfer ion and ammonia, which apparently has the composition 
Ag(NH3)2* and whose properties are distinct from those of the normal 
silver ion in water. So, we find that salts of this ion are much more 
soluble than those of the normal silver ion, particularly in the case of 
the halides. Similar complexes are formed in the case of many other 
salts dissolved in water in the presence of ammonia, as, for example, 
salts of copper, zinc, cobalt, nickel, etc. The distinctive properties of 
the complex affect all the characteristic properties of the resulting elec- 
trolytic solution. So the addition of ammonia to a solution of a silver 
or a copper salt in water decreases the viscosity of the solution, until all 



178 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the metal has been transformed to the complex. This behavior is due 
to the fact that the solutions of this complex possess a negative viscosity 
relative to that of pure water, while solutions of the original salt possess 
a positive viscosity with respect to pure water. 

In non-aqueous solutions, we find similar relations; that is, inter- 
action often takes place between the second solvent component and the 
electrolyte. Thus, the ionization of solutions of a large number of salts 
appears to be greatly affected by the addition of a small amount of water. 
This is particularly the case with electrolytes which exhibit a marked 
tendency to form complexes with water. If a salt, which exhibits a 
marked tendency to form hydrates, is dissolved in a medium, with 
which this salt has little tendency to form a solvate complex, then 
the salt will be relatively little ionized when dissolved in this solvent. 
On addition of water to such a solution, the salt apparently forms a 
complex with water, whose ionization in the original solvent is much 
greater than that of the anhydrous salt. Solutions of potassium chloride 
or iodide, for example, are highly ionized in acetone and their ionization, 
and consequently their conductance, is but little affected by the addition 
of water. On the other hand, lithium chloride, which shows a pronoimced 
tendency to form complexes with water, is ionized to only a relatively 
slight degree in pure acetone. On the addition of water to a solution 
of a lithium salt in acetone, the conductance is greatly increased. Similar 
results have been obtained in the case of calcium chloride. 

2. Conductance of Salt Solutions on the Addition of Small Amounts 
of Water. In Table LXIV are given values of the conductance of solu- 

TABLE LXIV. 
Conductance op Salts in Anhydkous Propyl Alcohol at 25°.^ 
Nal Ca (NO3) 2 Anhydrous 



CXIO' 


■A-mol 


cxio^ 


Atnol 


0.0623 


19.94 


0.363 


5.140 


0.1581 


19.36 


0.792 


3.834 


0.3902 


18.36 


1.617 


2.894 


0.6591 


17.72 


3.326 


2.184 


1.498 


16.30 


5.908 


1.798 


2.310 


15.40 


7.247 


1.688 


5.890 


13.23 


14.320 


1.258 


13.26 


11.28 


24.930 


0.976 


27.77 


9.815 


43.290 


0.772 


53.40 


8.400 







'EraUB and Bishop, J. Am. Chem. Eoc. iS, 1568 (1921). 



ELECTROLYTES IN MIXED SOLVENTS 179 

tions of calcium nitrate and sodium iodide in propyl alcohol. In the 
case of calcium nitrate the values given are the molecular conductances 
whose limit at low concentration should be approximately twice that of 
the equivalent conductance. It will be observed that while sodium iodide 
is highly ionized, calcium nitrate is ionized to only a relatively small 
extent. 

At a concentration of approximately 10"^ molal, the ionization of cal- 
cium nitrate is less than 15 per cent, whereas at the same concentration 
sodium iodide is very largely ionized. If the equivalent conductances are 
plotted against the concentrations, the curve of sodium iodide approaches 
a limiting form asymptotically, whereas that of anhydrous calcium nitrate 
is convex toward the axis of concentrations, the increase in conductance 
being the greater the lower the concentration of the electrolyte. 

The addition of 0.185 mols of water per liter to the calcium nitrate 
solution, whose concentration was 0.045 N, raised the conductance from 
0.772 to 2.036, and an additional 0.346 mols raised the conductance to 
2.991. It is evident, therefore, that the addition of water to a solution 
of anhydrous calcium nitrate in propyl alcohol causes a large increase 
in the ionization of the salt. This follows, since the viscosity of the 
solvent is not materially affected by the addition of small amounts of 
water. It is true that, if a complex is formed on the addition of water 
to a solution of calcium nitrate, the speed of the ion may be affected by 
the addition of water, but it seems likely that, if anything, the speed of 
the complex will be lower than that of the original ion. However this 
may be, it is very unlikely that the speed of the complex could vary 
greatly from that of the anhydrous ion and the resulting change in the 
conductance must therefore be due to a change in the ionization of the 
electrolyte as a result of the formation of a complex with water. 

TABLE LXV. 

Conductance of Mg(N03)2.6H20 in Anhydrous Propyl Alcohol and 
IN Propyl Alcohol Containing 0.7 Per Cent Water at 25°. 

Anhydrous Solvent Solvent + 0.7% Water 



cxio^ 


Amol. 


CXIO' 


A 


0.394 


12.422 


.298 


17.774 


0.865 


10.730 


1.950 


9.062 


1.942 


8.932 


3.758 


7.326 


3.483 


7.774 


6.339 


6.188 


6.406 


6.408 


11.670 


5.096 


9.804 


6.026 


19.460 


4.400 


19.89 


4.674 


30.410 


3.921 


36.12 


3.866 i- 


49.560 


3.555 



180 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In Table LXV are given values for the conductance of magnesium 
nitrate hexahydrate in anhydrous propyl alcohol and in propyl alcohol 
containing 0.7 per cent of water. 

The original salt having been hydrated, it is probable that the complex 
hydrate was to some extent present in the solution. Nevertheless, the 
value of the molecular conductance is of the same order of magnitude 
as that of anhydrous calcium nitrate in propyl alcohol and the conduct- 
ance curve is of the same general form. On the addition of water, the 
conductance of the magnesium nitrate is markedly increased, particularly 
in the more dilute solutions. The curve for the conductance in the 
presence of water twice intersects the curve for the conductance in the 
anhydrous solvent. This effect may in part be due to a change in the 
speed of the ions, owing to the presence of water, and in part to a more 
or less complex equilibrium which must exist between the dissolved 
electrolyte and the water. 

Those salts which have only a slight tendency to form stable com- 
plexes with water are, as a rule, ionized more highly in such solvents as 
acetone and the alcohols than are salts which exhibit a pronounced ten- 
dency to form stable complexes with water. Correspondingly, the addi- 
tion of water to a solution of a salt, which has little tendency to form 
complexes with water, has very little influence upon its ionization. The 
effect is scarcely observable in solutions of such salts as potassium and 
sodium iodides. In the case of lithium chloride dissolved in ethyl alcohol 
there is a slight increase in the ionization upon the addition of water. 
In Table LXVI are given values for the conductance of solutions of 
lithium chloride in ethyl alcohol in the presence of water.^ It is evident 
from an inspection of this table that the conductance of lithium chloride 
in ethyl alcohol is increased slightly upon the addition of water. The 
effect is somewhat more marked at higher concentration. 

TABLE LXVI. 

Conductance of LiCl in C2H5OH in the Presence of Water at 25°. 

Dilution 
of 
Cjj qMoIs per Liter Electrolyte 



1 2 10 V 

517.7 18.8 19.7 24.2 20 

•■(31.8 32.2 32.8 33.1 640 

2 Goldschmldt, Ztachr. f. pliys. Chem. 89, 138 (1914). 



A. 



ELECTROLYTES IN MIXED SOLVENTS 181 

3. The Conductance of the Acids in Mixtures of the Alcohols and 
Water. In aqueous solutions, the acids and bases occupy a unique posi- 
tion in that their solutions possess properties which, as a rule, differen- 
tiate them sharply from solutions of typical salts. The acids and bases 
in water are the only electrolytes which apparently conform to the mass- 
action law in this solvent. Furthermore, the ionization of different acids 
and bases differs greatly, while that of salts of the same type is prac- 
tically the same at all concentrations. So, also, the speed of the hydrogen 
and hydroxyl ions is much greater than that of the ordinary ions at ordi- 
nary temperatures. In the case of acids, at any rate, many facts indicate 
an interaction between acid and water whereby a complex positive ion 
is formed. 

In Table LXVII are given conductance values for solutions of hydro- 
chloric acid in methyl alcohol in the presence of varying amounts of 
water.* 

TABLE LXVII. 

Conductance of Hydhochloric Acid in Methyl Alcohol in the 
Presence of Varying Amounts op Water at 25°. 

Mols of HgO per Liter Cone, of 

0.1 0.2 0.5 1.0 2.0 Electrolyte 

. (115.4 99.6 91.3 81.6 78.1 67.1 0.10 

'^•••|171.9 141.7 129.3 120.8 116.7 97.8 0.0015625 

A„.. 192. 157. 143. 135. 130. 107. 0.00 



The effect of adding water to a solution of hydrochloric acid in 
methyl alcohol is to greatly decrease the conductance of the solution and 
this effect is relatively independent of the concentration of the solute. 
It appears, therefore, that the ionization of hydrochloric acid is not 
materially affected by the addition of water, but that the speed of the 
hydrogen ion is greatly reduced. It is true that on the addition of water 
to methyl alcohol the viscosity is increased, but the viscosity change due 
to the small amounts of water added in the case of these solutions is 
inconsiderable and cannot account for the large decrease in the conduct- 
ance of these solutions. Apparently, therefore, the change in conduct- 
ance is due to a slowing up of the hydrogen ion, since it is known that 
the chloride ion is normal in its behavior in mixtures of alcohol and 
water. The values given for the limiting value of the equivalent con- 
ductance are approximate, since the extrapolation function employed in 
determining these values is uncertain. 

• Goldschmidt and Thuesen, Ztschr. f. phys. Ohem. 81, 32 (1913). 



182 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Apparently, when water is added to a solution of hydrochloric acid 
in methyl alcohol, a complex is formed with water which moves with a 
much lower speed than does the normal hydrogen ion in pure methyl 
alcohol. It will be noted that the speed of the normal hydrogen ion in 
methyl alcohol is exceptionally high. The Ao values for typical salts 
in this solvent lie in the neighborhood of 100. The hydrogen ion must 
therefore move with a speed roughly three times that of the chloride or 
potassium ion. 

Solutions of hydrochloric acid in ethyl alcohol exhibit a similar 
behavior on the addition of water.* Values of the equivalent conduct- 
ance of hydrochloric acid in ethyl alcohol in the presence of varying 
amounts of water are given in Table LXVIII. 

TABLE LXVIII. 

Conductance of Solutions of Hydeochlobic Acid in Ethyl Alcohol 
IN THE Presence of Water at 25°. 

Mols of HaO per Liter 
0.028 0.05 0.1 0.2 0.5 1.0 2.0 3.0 Dilution 

. (74.2 63.2 68.5 52.6 47.4 42.8 41.8 42.4 44.4 1280 

^ 135.0 32.0 30.4 27.5 24.2 21.3 21.4 23.3 26.1 10 

A„.... 89.4 75.1 69.3 62.0 56.0 50.5 48.5 48.2 49.5 oo 

The conductance curve passes through a minimum for a solution contain- 
ing approximately two mols of water per liter. This minimum is slightly 
affected by the concentration of the acid. At lower concentrations the 
minimum occurs at a slightly higher concentration of water. The shift 
in the minimum point, following a change in the concentration of the 
acid, may in part be due to a change in the viscosity of the solution due 
to the addition of acid. On the other hand, it is possible that the ioniza- 
tion of the salt is materially affected by the presence of water, particu- 
larly at the higher concentrations. It may be assumed, however, that 
at very low concentrations of acid, the ionization is not materially 
changed due to the addition of water. If this is true, and the acid is 
highly ionized, the Ao values should follow a curve corresponding approxi- 
mately to that of the most dilute solution. In other words, the Aq values 
should pass through a minimum somewhere between 1 and 2 normal 
with respect to water, which has been found to be the case. This indi- 
cates that the addition of water results in an initial decrease in the 
speed of the ions up to a concentration of about 2 normal, and there- 
after in an increase on further addition of water. 

• Goldschmldt, Ztaohr. f. phya. Chem. 89, 132 (1914). 



ELECTROLYTES IN MIXED SOLVENTS 183 

This is further indicated by results at higher concentrations of water. 
In the following table are given values for the conductance of hydro- 
chloric acid in mixtures of water and ethyl alcohol at 25° for larger 
amounts of water.^ 

TABLE LXIX. 

Conductance of Solutions of Hydeochloeic Acid in Alcohol in the 
Peesence of Watee at 25°. 

Equivalent Conductances at Dilutions 



*^H,0 


7 = 12 


7 = 48 


7 = 


0.0 


34.3 


43.6 


67. 


6.83 


37.2 


43.0 


51. 


13.85 


60.3 


65.8 


75.5 


27.68 


115. 


121. 


130. 


41.57 


207. 


218. 


230.5 



The values for the pure solvent do not agree with those given in Table 
LXVIII. It is possible that the values in this case are low owing to 
the presence of traces of water." However, it is evident that, in the 
presence of water at higher concentrations, the conductance increases with 
addition of water. This may be due, in part, to an increased ionization, 
but it appears probable that it is also in part due to an increase in the 
speed of the hydrogen ion. That a complex between water and the 
hydrogen ions is initially formed is likewise indicated by other prop- 
erties of these solutions such as the catalytic effects due to the hydro- 
gen ion.' 

In the case of the weaker acids, on addition of water, the conductance 
curve is modified the more the weaker the acid. In Table LXX are given 
values for the conductance of sulphosalicylic acid in ethyl alcohol.* In 
solutions of sulphosalicylic acid, there is a marked decrease in the con- 
ductance on addition of small quantities of water up to normal concen- 
tration, but the effect is not as great as it is in solutions of hydrochloric 
acid. 

TABLE LXX. 

Conductance of Sulphosalicylic Acid in C2H5OH at 25° in the 
Peesence of Watee. 7 = 160. 

C-ar^ ■-.. .003 .019 .1 .2 .5 1.0 



'H,0 



2^ 



49.0 49.0 45.4 37.0 32.8 29.9 29.5 



"Kailan, ZtsoJir. f. phys. Ch^m. 89, 678 (1914). 

"Kalian, loc. cit. 

' Goldschmldt and Thuesen, loc. cit., p. 62. 

8 Goldschmidt, Ztschr. f. phys. Chem. 89, 139 (1914). 



184 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In the following table are given values for the conductance of picric 
acid in methyl alcohol in the presence of water.* 

TABLE LXXI. 

Conductance of Picric Acid in CH3OH at 25° in the 
Presence of Water. 



I 9. 
|56. 



Concentration of Water Cone. 

.5 1. 2. of Acid 

32 12.7 16.3 23.4 0.1 

73 63.7 70.2 75.7 0.0015625 



In this case, the conductance effect due to addition of water is the reverse 
of that in solutions of stronger acids. The conductance increases 
throughout as the concentration of water increases. It is evident that 
the ionization of picric acid is much smaller than that of the stronger 
acids. The increase in the conductance at the higher concentration is 
much more marked than it is at the lower concentration, indicating that 
at higher concentration, at least, an increase in the ionization due to the 
addition of water is a primary factor in causing an increase in the con- 
ductance of the solution. It may be presumed that the speed of the 
hydrogen ion is independent of the nature of the acid, and that conse- 
quently the Ao values for picric acid decrease with increasing amounts 
of water, until fairly high concentrations are reached. In the following 
table are given approximate values of Ao for picric acid dissolved in 
methyl alcohol in the presence of water.^" 

TABLE LXXII. 

Change of Ao for Picric Acid in Methyl Alcohol with Varying 
Amounts of Water. 



^H^O 





.5 


1. 


2. 


A 


182 


108 


98 


90 



These values of Ao, while only approximate, nevertheless cannot differ 
greatly from the true values and clearly indicate that the increase in 
the conductance of picric acid is due to an increased ionization of the 
acid as a result of the presence of water. 

In solutions of weaker acids, the effect of water on the ionization of 
the acid is even more pronounced. In the following table are given 
values for trichlorobutyric acid: ^^ 

• Goldschmldt and Thuesen, loc. cit., p. 35 
^'Ibid., loc. cit. 
^'IhU., loc. cit., p. 37. 



ELECTROLYTES IN MIXED SOLVENTS 186 

TABLE LXXIII. 

Conductance of 0.2 N Teichlorobutyeic Acid in CH3OH in the 
Presence of Water. 

Ch,0 10 2.0 

A 0.446 0.825 1.283 

In a 0.2 normal solution of this acid the conductance is increased 100 
per cent on the addition of one mol of water. In other words, the ioniza- 
tion is increased somewhat over 100 per cent by this addition of water. 
In this respect the acids behave in a manner similar to that of typical 
salts which have a great tendency to form hydrates. 

The effect of water on the ionization of the weaker acids is clearly 
shown in the increased value of the ionization constants of these acids 
on addition of water. In Table LXXIV are given values of the ioniza- 
tion constant ^^ for trichloroacetic acid in absolute alcohol and in alcohol 
containing 0.622 mols of water at different dilutions. Excepting at the 
highest concentrations, the constant varies but little with the concentra- 
tion of the acid. 

TABLE LXXIV. 

Ionization Constant of Trichloroacetic Acid in Alcohol in the 
Absence and in the Presence of Water. 





K X 10-" 




V 


Pure Alcohol 


Cjj = 0-622 N 


5.5 


5.03 




31.1 


11. 


4.74 




29.3 


22. 


4.45 




28.6 


44. 


4.45 




27.6 


88. 


4.50 




27.6 


176. 


— 




28.4 



It is evident that, due to the addition of 0.622 mols of water, the 
ionization constant of trichloroacetic acid is increased approximately six 
times. Corresponding to this increase in the value of the ionization con- 
stant of the acid, the conductance of the acid is obviously greatly 
increased. The effect of water on the conductance of different electro- 
lytes is shown in Figure 41. The great percentage increase in the con- 
ductance of trichloroacetic acid will be noted in contrast to a smaller 
increase in the case of picric acid and lithium chloride and a large decrease 
in that of hydrochloric acid. 

"Braune, Ztschr. f. phys. CJiem. 85, 170 (1913). 



186 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

It seems fairly clear that, on the addition of water to a solution of 
an acid in alcohol, a complex is formed between the acid and the added 
water. The hydrogen ion of this complex moves with a speed much 
lower than that of the normal hydrogen ion in alcohol or in pure water. 
In the case of the weaker acids, the ionization of the hydrated acid is 



60 


■ 








70 


■ 








60 










< 


\ 








g 50 

1 

3 

g 40 


■^_ 






— • ' y^aeo 


- 



















-4^ 

n 






i£C/ 




1 30 

'3 


PICmC ACID 






20 


-/ 








to 




TmCHLOHACCTIC AC 


1 





10 

Mols of Water, 



2.0 



3.0 



Fig.- 41. Illustrating the Influence of Water on the Conductance of Different 
Electrolytes in Ethyl Alcohol. 



much greater than that of the unhydrated acid. In solutions of salts in 
non-aqueous solvents, there is, as we have seen, a similar increase in 
ionization on the addition of water in the case of those salts which exhibit 
a pronounced tendency to form complexes with water. In these cases, 
therefore, the process of ionization is intimately connected with the 
formation of a more or less definite complex, and since these complexes 
are formed on the addition of a small amount of water to solutions in 



ELECTROLYTES IN MIXED SOLVENTS 187 

anhydrous solvents, there is all the more reason for believing that these 
complexes exist when the salts are dissolved in pure water. 

4. Conductance in Mixed Solvents over Large Concentration Ranges. 
A considerable number of systems have been studied in which salts 
have been dissolved in mixtures of two solvents miscible in all propor- 
tions. In these solutions the conductance has not been studied for small 
additions of either component. As a rule, the concentration was varied 
by intervals of 25 per cent. In such cases, the change in the viscosity of 
the medium, as well as that in the ionization of the electrolyte, makes 
itself felt. 

When the two solvents have approximately the same dielectric con- 
stant and the dissolved salts are ionized to practically the same extent 
in the two solvents, then the conductance of solutions in mixtures of these 
solvents is determined primarily by the viscosity of the mixtures. In 
other cases, where the viscosity change is small and the ionization of the 
salt in the two solvents differs greatly, the form of the curve is largely 
dependent upon the ionization change brought about by the change in 
the composition of the mixture. 

In Figure 42 are shown values of the fluidity of mixtures of acetone 
with water, methyl and ethyl alcohol at 0°.^* In Figure 43 are shown 
fluidity curves for mixtures of methyl alcohol with water and ethyl 
alcohol,"'* and nitrobenzol with methyl and ethyl alcohols," at 25°. The 
values are given in Table LXXV. In the case of these curves the precise 

TABLE LXXV, 

The Fluidity of Mixtures as a Function of Their Composition. 

Solvent Per Cent B 

A B 25 50 75 100 

HjO Acetone... 56.24 34.12 33.03 58.80 244.11 

CH3OH Acetone ... 122.2 153.9 187.4 222.2 244.1 j-i = 0° 
C2H5OH Acetone ... 53.88 96.08 147.0 200.4 244.lJ 



H2O CH3OH ... 112.3 76.18 67.72 83.6 144.41 

H2O C2H5OH .. 112.3 55.22 41.56 47.21 87.4 

CeH.NO^ CH3OH ... 54.29 84.4 110.9 142.3 166.4 

CeH^NOa C2H5OH .. 54.3 73.3 82.7 88.2 87.4 

C2H5OH CH3OH ... 87.36 105.5 124.9 147.3 164.4 



t = 25° 



values are represented only for the pure solvents and the mixtures hav- 
ing compositions of 25, 50 and 75 per cent, smooth curves having been 

"Jones, Bingham and McMaster, Ztschr. f. phys. Cltem. 5t, 193 (1906). 
" Jones and Veazey, Conductivity and Viscosity in Mixed Solvents, Carnegie Reports, 
p. 196 (1907). 

"Jones and Veazey, Ztschr. /. phya. Ohem. 62, 49 (1908). 



188 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

drawn through these points. At intermediate concentrations the true 
curves may vary considerably from the curves as drawn, particularly at 
concentrations in the neighborhood of the axes. Nevertheless, the curves 
show in a general way the relation between the fluidity and the com- 
position of these mixtures. The fluidity curves of all mixtures in which 




25 SO ?£■ 

Perf? Cent RcetonE 



lOO 



Fig. 42. Representing the Fluidity of Mixtures of Acetone with Various Solvents at 
0° as a Function of Composition. 



water is one component are characterized by a pronounced minimum, 
which lies roughly at a composition of 50 per cent. When the fluidity 
of the second solvent differs greatly from that of water, the minimum 
is displaced in the direction of the solvent having the lower fluidity. In 
mixtures of solvents of the same type, such as methyl and ethyl alcohols, 
as well as in mixtures of the alcohols and nitrobenzol, or the alcohols and 
acetone, the curves approach more or less closely to straight lines, the 
viscosity of the mixture being throughout intermediate between that of 



ELECTROLYTES IN MIXED SOLVENTS 189 

the two components. When the two components have nearly the same 
fluidity, the fluidity curve exhibits a slight minimum. 

It is apparent that the fluidities of mixtures in general differ con- 
siderably from those of the pure components and it is to be expected that 
the conductance of solutions in such mixtures will be materially affected 
by the viscosity change of the solvent. In those cases in which the elec- 




Fe"^ CetJT OF CsMpotfetfr B. 

Fig. 43. Fluidity of Various Mixtures at 25°. 

trolyte is largely ionized, it is to be expected that the conductance of a 
solution in a mixture of two solvents will vary approximately in accord- 
ance with the fluidity of the mixture. At higher concentrations a similar 
correspondence between the conductance and the fluidity is to be expected 
when the ionization of the electrolyte is the same in the two solvents. In 
general, this will be the case when we have solvents which have the same 
dielectric constant, and an electrolyte which does not exhibit a marked 
tendency to form solvates. In other cases, when the ionization is 



190 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

largely dependent upon the formation of solvates between the electrolyte 
and one or the other of the solvent components, the ionization of the ■ 
salt in the mixture, rather than the fluidity of the mixture, will determine 
the form of the conductance curve and this will be the more true, the 
more nearly the fluidity curves are linear functions of the composition. 

In Figure 44 are shown conductance curves for solutions of tetra- 
ethylammonium iodide in mixtures of water ^* with methyl and with 




Fig. 44. 



Per Cent of Component B. 

Conductance of Tetraethylammonium Iodide in Solvent Mixtures at 25° 
at F = 800. 



ethyl alcohol, nitrobenzol " with methyl and with ethyl alcohol, and 
methyl with ethyl alcohol.^' The data from which the curves are drawn 
are given in Table LXXVI. 

Comparing the conductance curves with the fluidity curves, it is clear 
that in these solutions of tetraethylammonium iodide there is a close 
correspondence between the two. The conductance curves for mixtures 
of methyl alcohol, ethyl alcohol and nitrobenzol correspond very closely 
with the fluidity curves. So, also, in mixtures of water with ethyl and 

" Jones, Bingham and McMaster, loc. cit., p. 257. 
" Jones and Veazey, loc. cit., p. 44. 



ELECTROLYTES IN MIXED SOLVENTS 191 

TABLE LXXVI. 

Conductance of Tetraethylammonium Iodide in Mixed Solvents 
AT 25° AT A Dilution of 800 Liters. 



Soh 


/ent 






Per Cent B 




A 


B 





25 


50 


75 


100 


H^O 


CH3OH .. 


. 100.6 


67.03 


55.17 


62.50 


105.3 


H^O 


C2H5OH . 


.. 100.6 


54.53 


38.68 


35.51 


41.46 


CeH,NO, 


CH3OH .. 


. 3L44 


47.91 


63.54 


80.53 


105.3 


CeH.NO, 


C^H^OH . 


.. 3L34 


37.88 


41.87 


43.51 


41.46 


C,H,OH 


CH3OH .. 


. 41.46 


55.20 


69.44 


84.22 


105.3 



methyl alcohols, a pronounced minimum is found in both conductance 
curves. Finally, in mixtures of nitrobenzol and ethyl alcohol, the con- 
ductance curve exhibits a slight maximum corresponding with the maxi- 
mum in the fluidity curve. In general, salts which show little tendency 
to form stable complexes with water, in other words, those salts which 
exhibit a negative viscosity in aqueous solutions, yield conductance 
curves closely resembling those for tetraethylammonium iodide. It may 
be noted, however, that the conductance for tetraethylammonium iodide 
in methyl alcohol is abnormally high, being in fact somewhat greater 
than that of the same salt in water. In general, the conductance of salts 
in methyl alcohol is somewhat lower than that of salts in water, even 
though the viscosity of water is greater than that of methyl alcohol. The 
curves for solutions of other binary salts do not differ materially from 
those of tetraethylammonium iodide. In the case of electrolytes of this 
type, the ionization in a given solvent is near the maximum and is not 
appreciably affected by the addition of a small amount of another solvent. 
Moreover, the ionization of typical salts in these solvents does not differ 
greatly at concentrations approaching 10"^ normal. The form of the 
conductance curves, therefore, is determined primarily by the fluidity 
of the solvent mixtures. 

TABLE LXXVII. 

Conductance of Solutions of Potassium Iodide in Mixtures of 
Acetone with MeIhyl and Ethyl Alcohols and Water at 0°. 

Per Cent Acetone . . 25 50 75 100 

H^O 78.0 47.8 37.5 44.1 120.0] 

CH3OH 71.7 83.9 94.1 106.5 120.0^7=1600 

C2H5OH 28.6 40.1 61.3 84.8 120.oJ 

H,0 76.7 44.6 36.3 41.6 100.4"1 

CH,OH 65.7 74.1 82.7 93.1 100.4^7 = 200 

C2H5OH 22.0 35.5 52.2 72.0 IOO.4J 



192 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In Table LXXVII are given values for the conductance of potassium 
iodide at 0° in mixtures of acetone with methyl and ethyl alcohols and 
water " at the concentrations V = 1600 and V = 200. The results are 
shown graphically in Figure 45. It is apparent that in solutions of potas- 
sium iodide in mixtures containing acetone, the general form of the con- 
ductance curves corresponds with that of the fluidity curves. However, 
the deviations from the fluidity curves in these solutions are considerably 




as so 

Per Cent Acetone. 



loo 



Fig. 45. 



Conductance of Potassium Iodide in Acetone Mixtures at 0° at Dilutions 
F = 200 and 7=1600. 



greater than in solutions of tetraethylammonium iodide in mixtures of 
the alcohols and water. This is doubtless due to the relatively low 
ionizing power of acetone and its selective action upon different electro- 
lytes, as welLas upon the exceptionally high value of the fluidity of pure 
acetone with respect to that of the other solvents. The concentration 
change from a dilution of 1600 to 200 has only an immaterial influence 
upon the form of the curves. 

The ionization of acetone solutions of salts which exhibit a marked 
tendency to form complexes with water, or other solvents, is very low. 
Under these conditions, the change in the ionization of the electrolyte due 

" Jones, Bingbam and McMaster, loo. cit., p. 193.- 



ELECTROLYTES IN MIXED SOLVENTS 



193 



to the addition of a second solvent becomes apparent. In Table 
LXXVIII are given values for the conductance of lithium bromide in 
mixtures of acetone with methyl and ethyl alcohols and water.^* 

TABLE LXXVIII. 

The Conductance of Lithium Bromide in Mixtures of Acetone 
WITH Methyl and Ethyl Alcohols and Water at 0°. 



Per Cent Acetone 



H,0 



56.12 



CH3OH 57.63 

CjH.OH 20.79 

HjO 47.25 

CH3OH 35.92 

C.H^OH 10.55 



25 
35.71 
60.38 
29.21 

28.82 
35.03 
14.72 



50 
28.34 
67.02 
50.98 
21.70 
34.27 
19.23 



75 
31.65 
84.15 
66.28 
24.00 
29.77 
19.16 



100 
70.891 
70.89 ^F: 
70.89] 
11.911 

11.9UF: 

11.91J 



1600 



10 



The results are shown graphically in Figure 46. An examination of 
the curves shows a very complex behavior on the part of these solutions 
compared with that of solutions of potassium iodide in the same solvents. 
In mixtures of acetone and methyl alcohol, at the lower concentration, 





1 I 1 — 


CH50M 

H..O 


' /""/' 


CH3OH 
C^HfOH 


1 1 1 



100 



80 



V" i«oo 



'- 60 



■ 40 



3 

O 
O 



> 

'3 



to 



25" 



SO 75 

Per Cent Acetone. 



100 



Fig 46 Conductance of Lithium Bromide in Acetone Mixtures at 0° at 
F = 10 and F = 1600. 
" Jones Bingham and McMaster, loc. cit., p. 257. 



194 /PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the conductance curve exhibits a pronounced maximum. The curve for 
ethyl alcohol mixtures exhibits a pronounced inflection point, while that 
for water merely exhibits a minimum corresponding to the minimum in 
the fluidity curve of the mixtures of acetone and water. At the higher 
concentration, the curve for water initially rises steeply to a very flat 
maximum and minimum, after which it rises with increasing concentra- 
tion of water, the curve corresponding roughly to the fluidity curve of the 
mixtures within the region of these compositions. The conductance of 
solutions in mixtures of acetone and methyl alcohol rises sharply for 
initial additions of methyl alcohol, after which it remains practically 
constant until the axis of the pure methyl alcohol is reached. With ethyl 
alcohol the conductance likewise increases markedly for the initial addi- 
tions. Thereafter, the curve passes through a maximum, after which it 
gradually diminishes to the final value of the conductance in pure ethyl 
alcohol. It is only in solutions in which the percentage of ethyl alcohol 
has fallen as low as 25 per cent that the curves begin to approach in form 
the fluidity curves of the mixtures. For mixtures containing larger 
amounts of acetone the form of the curve is due largely to the change in 
the ionization of the electrolyte. On the addition of a second solvent to 
acetone, the ionization of lithium bromide is greatly increased. In the 
water mixtures, the viscosity is increased so greatly for small additions 
of this solvent that the conductance diminishes. In the case of methyl 
alcohol, however, the fluidity is only slightly reduced by the addition of 
alcohol and consequently the conductance curve rises initially due to the 
increased ionization of the salt. At higher concentrations of alcohol, 
however, the increasing viscosity of the solvent finally makes itself felt 
and the conductance again falls. At the higher concentration of the salt, 
the addition of water causes a sufficient increase in the ionization of the 
electrolyte to overbalance the decrease due to the decreasing fluidity of 
the mixture. Initially, therefore, the conductance curve for lithium 
bromide in the mixture increases with the addition of water, passing 
through a slight maximum, after which the curve approximates the 
fluidity curve of the solvent. 

As a rule, higher types of salts are ionized to a much smaller extent 
than are binary electrolytes, particularly the salts of metals which exhibit 
a pronounced tendency to form solvates with water. In Table LXXIX 
are given values for the conductance of calcium nitrate in mixtures of 
acetone with methyl and ethyl alcohols and water.^" 

The relation between the conductance and the composition of these 
mixtures is shown graphically in Figure 47. It is evident that solutions 
of calcium nitrate in mixtures containing acetone present a very complex 

" Jones, Bingham and McMaater, Iqc. Ht., p. 193. 



ELECTROLYTES IN MIXED SOLVENTS 



195 



TABLE LXXIX. 

Conductance of Solutions of Calcium Nitrate in Mixtures of 
Acetone with Methyl and Ethyl Alcohols and Water at 0°. 

25 50 75 100 

80.0 66.2 76.7 10.361 

82.6 79.2 64.2 10.361f=1600 

31.6 38.0 36.2 10.36J 

55.0 42.2 31.3 4.441 

17.76 13.82 8.10 4.44[y=10 

6.01 6.00 4.80 4.44 



Per Cent Acetone 

H^O 128.3 

CH3OH 77.2 

C,H,OH 18.81 



H,0 



89.8 



CH3OH 18.98 

C^H^OH 5.13 



relation between conductance and composition. This is particularly true 
of the acetone-water mixtures. Solutions of calcium nitrate in acetone 
are ionized to a very slight extent, even at high dilutions. The limiting 
equivalent conductance of binary electrolytes in acetone has a value of 
approximately 170. The limiting value of the equivalent conductance of 



HtO 



CHjOH ■^ 



CH3OH 



CiH.Ort 



1 — 


1 1 


ISO 






las 






too 








\ \ 










75 


\ 
\ 

\ 


•fc \ I 


so 


: "■"''^ 


\ \ \ 


£5 




v» re 


. 






3 

a 
o 
O 



3 
cr 



o as so 7s 100 

Per Cent Acetone. 

Fig 47 Conductance of Calcium Nitrate in Acetone Mixtures at 0° at 
F = :0 and F = 1600. 



196 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

calcium nitrate is obviously of the same order. Even at a dilution of 
1600 liters, therefore, calcium nitrate is ionized less than 10 per cent. 
The addition of hydroxy-compounds, which tend to form stable complexes 
with calcium salts, causes an enormous increase in the conductance of 
solutions of this salt in acetone, even though the amount of the second 
component added is relatively small. The curves as drawn are only 
rough approximations and it is not improbable that the initial conduct- 
ance increase is even greater than indicated in the figure. Owing to the 
increased ionization of calcium nitrate on the addition of water, there- 
fore, the conductance rises enormously, even though the speed of the ions 
is greatly depressed on the addition of water. As a consequence, the con- 
ductance curve on addition of water passes through a pronounced maxi- 
mum at a composition at or above 75 per cent of acetone. On the 
addition of further amounts of water, the conductance curve follows, 
roughly, the fluidity curve of the solvent mixture. The addition of 
methyl alcohol likewise results in an increase in ionization, although this 
increase is much lower than in the case of water. The conductance curve, 
therefore, passes through a comparatively flat maximum at a composition 
in the neighborhood of 25 per cent of acetone. The ionization of calcium 
nitrate dissolved in a mixture of methyl alcohol and acetone therefore 
has not reached a value corresponding to that of a normal electrolyte, 
even when as much as 75 per cent of methyl alcohol has been added. 
The addition of ethyl alcohol causes a marked increase in the conductance, 
although considerably less than that due to methyl alcohol. The curve 
passes through a distinct maximum, after which the conductance de- 
creases, chiefly owing to the decrease in the fluidity of the mixture. 

At the higher concentration, the curves are greatly modified. Again, 
the ionization of the electrolyte is greatly increased on addition of the 
second solvent, as is indicated by a marked increase in the conductance 
of the solutions. In the case of water, the curve exhibits a marked inflec- 
tion point in the neighborhood of the composition containing 50 per cent 
of alcohol and water. At these higher concentrations, therefore, solu- 
tions of calcium nitrate in mixtures of acetone and water exhibit an 
ionization much below that of normal electrolytes. The curve, on addi- 
tion of methyl alcohol, shows a continuous increase in the conductance 
throughout its course. That for ethyl alcohol shows a slight increase 
only, the curve exhibiting a very flat maximum. At the higher concen- 
trations of the salt, therefore, the addition of ethyl alcohol causes only 
a relatively small increase in the conductance of calcium nitrate. Actu- 
ally, however, the ionization is considerably increased on the addition of 
ethyl alcohol, since the fluidity of the ethyl alcohol mixture is much lower 
than that of pure acetone. 



ELECTROLYTES IN MIXED SOLVENTS 197 

Extensive data are available which show that the examples given 
above are typical of the behavior of solutions of electrolytes in mixed 
solvents. The data do not have sufficient precision to make it possible 
to determine the values of Ao in the mixtures, for which reason it is 
necessary to consider only the general outline of the conductance curves. 
It is evident that, in the case of solutions of salts which are highly ionized, 
the conductance curves parallel the fluidity curves. If, however, the 
electrolyte is only slightly ionized in one of the solvents, the addition of 
the second component may cause a large shift in the conductance values 
due, primarily, to a large change in the ionization of the electrolyte. It 
should be noted that, whenever the fluidity of the solvent medium 
changes, whether under the action of pressure or temperature, or whether 
through a change in the viscosity of the medium due to the presence of 
the electrolyte itself or due to the presence of a non-electrolyte, the con- 
ductance is affected by the viscosity change, and, while the conductance 
may not change in direct proportion to the fluidity change of the medium, 
nevertheless the effect of fluidity change is very marked. These facts are 
in entire accord with our notions as to the nature of the conduction 
process. On the other hand, it is clearly evident that the conductance is 
likewise dependent upon some other factor, namely the ionization. The 
ionization is a function, in the first place, of the dielectric constant of 
the solvent medium, as well as of the concentration of the electrolyte. 
In the second place, however, the ionization is greatly affected by inter- 
action between the dissolved electrolyte and the solvent medium. Ap- 
parently, complexes are formed between the dissolved electrolyte and the 
solvent, which are largely ionized. Certain solvents, such as acetone, 
for example, appear to have a very small tendency to form complexes. 
When salts, which exhibit a marked tendency to form complexes, are 
dissolved in solvents of this type, the resultmg ionization is relatively 
low. This effect is marked in the case of salts of the alkali metals. 
Salts of sodium, potassium, rubidium and caesium are very largely 
ionized in all solvents, apparently without exception, whereas the salts of 
lithium exliibit a markedly lower ionization in many solvents, as for 
example in acetone. As is well known, lithium salts exhibit a great 
affinity for hydroxy-solvents, and apparently the formation of a complex 
is a necessary condition for ionization in the case of salts of this type. 

In comparing the ionizing power of different solvents, therefore, it is 
necessary to select such electrolytes as exhibit the least tendency to form 
complexes. This has in general been done by various writers on this 
subject. Nevertheless, it should be borne in mind that the possibility 
always exists that a given electrolyte in a given solvent may exhibit 
exceptional properties. 



Chapter YIII. 
Nature of the Carriers in Electrolytic Solutions. 

1. Interaction between the Ions and Polar Molecules. The results 
given in the preceding chapter indicate that an equilibrium exists between 
the ions, and possibly the un-ionized fraction, of a dissolved electrolyte 
and the molecules of an added non-electrolyte of the polar type. If 
reactions of this type take place between a non-electrolyte and an elec- 
trolyte, both of which are present in relatively small amounts in the 
solvent medium, then there is all the more reason for believing that 
reaction takes place between the electrolyte and the non-electrolyte when 
the latter is present in large excess. Apparently, the ions in solution do 
not consist merely of the charged groups present in the original salt, 
but rather of these groups associated with the solvent. Where the ions 
possess great tendency to form definite complexes with the solvent, as is 
the case, for example, with the calcium ion in water and the silver ion in 
ammonia, a portion of the solvent is present in the form of a definite 
chemical compound. In addition to this, however, an ion may con- 
ceivably be associated with a further amount of solvent as a result of the 
charge on the ion and the electrical moment of the solvent molecules. 

2. Hydration of the Ions in Aqueous Solution. It has been defi- 
nitely established that in aqueous solutions certain ions are hydrated; ^ 
that is, in passing through the solution they carry water with them. 
Since the conductance values of all ions in water are of the same general 
order of magnitude, it follows that all ions are in all likelihood hydrated, 
save, perhaps, the highly complex ions. 

If the ions are hydrated, then, in the course of a transference experi- 
ment, water will be transferred toward one electrode or the other. If 

Ntg represents the number of molecules of water associated with the 



w 

1 and A 

W 



anion and iV^ the number of molecules of water associated with the 
cation and if T^ is the fraction of the current carried by the anion, that 

'Lobry de Bruyn, Bee. Trav. Chim. 22, 430 (1903) ; Morean and KnnnH- t a^ ni.„^ 
Soo. B8, 572 (1906) ; Buchbock, Ztachr. //pAj/s. C7,em 55^5f^(1906^ Waahbui ' 7 
Ohem. 800. 31, 322 (1909) ; Wasbburn and Millard, J. Am. Chem.Soc. S7 694 (1915)" 

198 



CARRIERS IN ELECTROLYTIC SOLUTIONS 199 

is, if this is the true transference number of the anion, and if T^ is the 

true transference number of the cation, then according to Washburn^ 
the net transfer of water per equivalent of electricity passing through 
the solution will be: 

(47) T'JN^ —T^N"' =N^, 

^ t w t w w' 

where N is the net transfer of water per equivalent of electricity. 

In general, therefore, the passage of a current through a solution will 

be accompanied by a net transfer of water, whose value is N per 

equivalent of electricity. This transfer of water may be determined by 
introducing into the solution a substance which itself takes no part in 
the transfer of the charge. The change in the concentration of the water 
with respect to this reference substance will give the transfer of water, 
and the change in the concentration of the salt with respect to the same 
reference substance will give the true transference number of the salt at 
the same time. It follows, therefore, that if the true transference num- 
ber of the salt and the net transference number of the water are known, 
the relative amounts of water associated with the two ions may be deter- 
mined. As ordinarily carried out, transference experiments in which 
water is employed as reference substance yield, not the true transference 
number, but a transference number differing therefrom by an amount 
depending upon the relative amount of water transferred. The relation 
between the true and the ordinary transference number is given by the 
equation: 

(48) ^?=n+<(r-)' 



where T^ is the ordinary transference number of the cation and 






is the ratio of the number of mols of salt to that of water in the solution. 
If transference measurements on various electrolytes with a common ion 
are carried out, then the relative hydration of the uncommon ions may 
be determined. The absolute hydration of the ions is of course not 
determinable. In Table LXXX are given values of the true transference 
number, the ordinary transference number, and the water transference 



' Washburn, loo. cit. 



200 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

number for different electrolytes in water at a concentration of 1.2 
normal at 25°. 

TABLE LXXX. 

Thansference Numbers of Electrolytes and Solvent For 
Aqueous Solutions. 



rf 


HCl 
0.844 


CsCl 
0.491 
0.485 
0.33 


KCl 
0.495 
0.482 
0.60 


NaCl 
0.383 
0.366 
0.76 


LiCl 
0.304 


t 

rpC 


0.820 


0.278 




< 


0.24 


1.5 



In solutions of these electrolytes, the net transfer of water takes 

place from the anode to the cathode, as shown by the values given in the 

F 
table for N . In these cases, correspondingly, the true transference 

numbers of the cations are larger than the ordinary transference num- 
bers. It is obvious from Equation 48 that, as the concentration of the 
solution decreases, the ordinary transference number approaches the 
true transference number. The relation between the water carried by 
the cation and that by the chloride ion is evidently given by the fol- 
lowing equations: 

iV^ =0.28+1.085 N^\ 
iV^^= 0.67 + 1.03 N^\ 
(49) ivj =1.3 +1.02 n2\ 

^Na^2.0 +1.61 N^\ 
ivj;* =4.7 +2.29 N^^, 

Since the hydration of the chloride ion is not known, the absolute hydra- 
tion of the various cations may not be determined. If, however, a value 
is assumed for the hydration of the chloride ion, then the hydration of the 
other ions may at once be calculated by means of these equations. The 
values of the hydration of the different cations for different assumed 
values for the hydration of the chloride ion are given in the following 
table: 



CARRIERS IN ELECTROLYTIC SOLUTIONS 201 

TABLE LXXXI. 

Calculated Hydration of the Ions for Different Assumed Values 
FOR THE Hydration of the Chloride Ion. 



w 


w 




w 


w 


«t' 



4 
9 


0.28 

1.0 

2.0 


0.67 

4.7 

9.9 


1.3 

5.4 

10.5 


2.0 

8.4 

16.6 


4.7 
14. 
25.3 



The assumption that the chloride ion is un-hydrated is improbable, 
since the conductance of the chloride ion is very nearly equal to that of 
the potassium ion. The value assumed for the hydration of the chloride 
ion should therefore differ little from that of the potassium ion. This 
necessitates assuming for the chloride ion a value not materially less 
than 4. In all likelihood the true value lies somewhere between 3 and 9, 
although the true value must necessarily remain uncertain. Below are 
given the values of the ionic conductance for the different ions at 18°, 
together with the ratio of these conductances to that of the hydrogen ion. 

TABLE LXXXII. 

Comparison op Ionic Conductances and Hydration Numbers. 

^Cl ^H ^Cs ^K ^Na ^Li 
w w w w w w 

Hydration No 4.0 1.0 4.7 5.4 8.4 14.0 

Ionic Cond 65.5 315. 68.0 64.5 43.4 33.3 

315/A 4.8 1.0 4.6 4.9 7.3 9.5 

It is seen that the values of the ionic conductances relative to that 
of the hydrogen ion correspond roughly with the values of the hydration 
of the different ions, assuming the hydration of the hydrogen ions to be 
unity. An exact correspondence between the hydration and the con- 
ductance is not to be expected. Nevertheless, except in the case of the 
caesium and the chloride ions, the order of the reciprocal conductance 
values corresponds with the order of the hydration numbers. The 
chloride, caesium, and potassium ions are among the most rapidly mov- 
ing ions in water, excepting the hydrogen and hydroxyl ions, and it may 
therefore be concluded that all ions in water are hydrated at least as 
much as the chloride ion. It is possible, of course, that the hydration 
numbers may be considerably larger than those assumed on the basis 
of an hydration of 4 for the chloride ion. How the hydration of the ions 



202 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

varies with the temperature and the concentration is not known. If 
the absolute hydration of the ions is large, then it is to be expected that 
the hydration will change at higher concentrations. It is possible, 
therefore, that at concentrations below 1.2 normal the hydration of the 
ions may be considerably greater than at the higher concentration. 

As we have seen in an earlier section, at higher temperatures the 
conductance of the more rapidly moving ions approaches that of the 
more slowly moving ions. At the same time, as we have seen, the con- 
ductance of the more slowly moving ions changes almost in exact pro- 
portion to the fluidity change of the solvent. It may be concluded, 
therefore, that, at higher temperatures, the hydration of the more rapidly 
moving ions increases and approaches that of the more slowly moving 
ions, such as that of the lithium ion. It is probable, therefore, that as 
the temperature increases the net transference of water diminishes, while 
the absolute amount of water associated with the ions increases. 

3. Calculation of Ion Dimensions from Conductance Data. Lorenz^* 
has calculated the ion dimensions from the ion conductances, by means 
of the Einstein-Stokes ^^ equation. The values obtained for the ion 
dimensions have been compared with those obtained by other methods, 
as determined from the density of substances in a condensed state, assum- 
ing close packing of the molecules. For ions containing a large number 
of atoms, particularly large organic anions and cations, the calculated 
values from the conductance data agree well with those derived by other 
methods. In the case of the simpler ions, however, a similar agreement 
has not been found. In the case of the alkali metals, for example, 
lithium, which has the smallest atomic volume, has the lowest conduct- 
ance, while caesium, with the largest atomic volume, has the highest 
conductance. It has generally been assumed that the reversal in the 
order of the conductance of the ions of the alkali rnetals is due to 
hydration. 

Born 2° and Lorenz ^^ consider that the Einstein-Stokes equation is 
applicable even in the case of small ions and that the observed diverg- 
ence is due to electrical interaction between the charge on the ions and 
the adjacent solvent molecules. This electromagnetic frictional effect 
is the greater, the smaller the volume of the ion. The total frictional 
effect which the ion experiences is thus the sum of two effects, one of 
which decreases and the other of which increases with decreasing ionic 
diameter. The function which expresses the ionic resistance in terms 

i" Lorenz, Ztachr. f. Elektroch. 20, 424 (1920) ; Ztschr. 1. phys. Chem. 73. 252 (1910) ■ 
also, numerous articles in the Ztschr. f. Anorg. Chem. 
""Einstein, Ann. d. Phys. It, 549 (1905). 
s" Born, Ztschr. f. Elektroch. 26, 401 (1920). 
"^ Lorenz, loo. cit. 



CARRIERS IN ELECTROLYTIC SOLUTIONS 203 

of the ionic diameter therefore passes through a minimum. In this way- 
Born accounts for the diminishing values of the ion conductance with 
decreasing volume in the case of the simpler ions. 

The constants involved in the equation for the electro-frictional effect 
are somewhat uncertain. In any case, these constants should depend 
solely upon the properties of the solvent medium, assuming an ion of 
fixed dimensions. 

The correctness of this theory appears somewhat doubtful. In the 
first place, it is difficult to account for the fact that at higher tempera- 
tures the ion conductances in aqueous solutions approach the same value. 
While it is true that the dielectric constant of the medium varies with 
the temperature, an effect of the. order of that observed in aqueous solu- 
tions is scarcely to be expected. More convincing, perhaps, is the rela- 
tion of the ion conductances in non-aqueous solutions. If the theory of 
Born and Lorenz is correct, the order of the ion conductances should be 
the same in different solvents. This is by no means the case. For exam- 
ple, as may be seen from the values of the ion conductances in liquid 
ammonia given in an earlier chapter, the conductance of the silver ion 
is markedly lower than that of the sodium ion in ammonia; while in 
water the conductance of the sodium ion is much smaller than that of the 
silvfer ion. Again, the conductance of the ammonium ion in ammonia is 
practically identical with that of the sodium ion, whereas the conduct- 
ance of the ammonium ion in water is almost identical with that of the 
potassium ion. While the conductance of the lithium ion in water is 
much smaller than that of the silver ion, the conductance of the lithium 
ion in ammonia differs but little from that of the silver ion. So, also, 
in the case of anions, the conductance of the nitrate ion is identical with 
that of the iodide ion in ammonia, while in water it is much smaller. 
Similarly, the conductance of the chloride ion in ammonia is markedly 
greater than that of the iodide ion; whereas in water the conductance of 
the iodide ion is greater than that of the chloride ion. An examination 
of the conductance values of electrolytes in other non-aqueous solvents 
shows that here, too, the order of ion conductances is a characteristic 
property of the solvent medium and of the dissolved electrolytes. For 
example, in acetone the conductance values of the lithium, sodium and 
potassium ions are practically identical; while the conductance of the 
ammonium ion is markedly greater than that of the potassium ion. 
While in water the conductance of the sulphocyanate ion is markedly 
lower than that of the iodide ion, in acetone the conductance of this ion 
is greater than that of the iodide ion. So, also, in pyridine the con- 



204 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ductance of the sulphocyanate ion is markedly greater than that of the 
iodide ion. 

It is evident that, applied to solutions in non-aqueous solvents, the 
theory of Born and Lorenz meets with great difficulties. The values of 
the ion conductances in different solvents are in much better agreement 
with the assumption that the differences in the ion velocities of the 
simpler ions are primarily due to the size and nature of the complexes 
formed between the ion and the solvent medium. An ion will, in gen- 
eral, exhibit a low conductance in a medium with which it has a great 
tendency to form stable complexes. On the other hand, in media with 
which the tendency to form complexes is less pronounced, its conductance 
will be relatively high. Thus, the silver and ammonium ions in ammonia 
have a relatively low conductance; while in acetone, sodium and lithium 
have a relatively high conductance. The properties of solutions of these 
salts in the solvents mentioned indicate a high solvation in ammonia 
solutions and a low solvation in acetone solutions. 

It has been demonstrated by means of, transference measurements in 
aqueous solutions that the alkali metal and hydrogen ions are hydrated. 
While the absolute degree of hydration remains uncertain, it is probably 
safe to assume that the hydration of the hydrogen ion is not less than 
unity, which requires a hydration in the neighborhood of 5 for the 
potassium ion and 14 for the lithium ion. 

As we have seen in Chapter V, the relation between the conductance, 
i.e., the speed of an ion, and the viscosity of the medium through which 
it moves is anything but simple. The conductance of ions of small 
dimensions is not proportional to the fluidity of the ionizing solvent. 
On the addition of a second non-ionic component, the conductance change 
of the ion is approximately proportional to the fluidity change of the 
medium only when the molecules of the added substance are small. 
When the dimensions of the molecules of the added substance are large 
compared with those of the ions, the conductance change is invariably 
smaller than the fluidity change. 

Finally, Dummer ^^ has measured the diffusion coefficients of a num- 
ber of organic solvents of varying molecular volume in one another and 
compared his results with one another by means of the Einstein-Stokes 
equation. The molecular dimensions found for the same substance in 
different solvents do not agree well with one another. The Einstein- 
Stokes equation should be applied with caution to systems of particles 
of molecular dimensions. 



CARRIERS IN ELECTROLYTIC SOLUTIONS 205 

4. The Hydrogen and Hydroxyl Ions. In aqueous solutions, the 
hydrogen and hydroxyl ions appear to occupy a more or less unique 
position. They are characterized by the exceptionally high value of their 
ionic conductance. At 0°, the hydrogen ion moves approximately 10 
times as fast as the acetate ion, or approximately 5 times as fast as the 
potassmm ion. At the same temperature the hydroxyl ion moves from 
5 to 6 times as fast as the acetate ion. The question as to the cause of 
the high values for the conductance of these two ions in water naturally 
arises. A more or less obvious explanation is: that these ions are 
hydrated to a much smaller extent than are the other ions; or, in other 
words, they are relatively smaller than the other ions. This view, more- 
over, is supported by the results obtained from transference experiments. 
As was shown in the preceding section, the amount of water associated 
with the hydrogen ion is much smaller than that associated with any 
other positive ion for which data exist. It might be expected, therefore, 
that the speed of the hydrogen ion would have an abnormally high value 
because of its low hydration. Presumably, a similar explanation would 
hold in the case of the hydroxyl ion, although here we have no data as 
to the relative hydration. That the hydrogen ion is in fact hydrated, 
admits of no question. The minimum amount of water which might be 
associated with the hydrogen ion is 0.28 mol. It is improbable, how- 
ever, that hydrogen ions exist in water unassociated with water molecules. 
In an earlier section it was shown that the addition of water to alcohol 
solutions of the strong acids greatly diminishes the conductance of the 
acid, while the addition of water to a solution of a weak acid greatly 
increases the conductance of the acid. It may be inferred from this that 
a complex is formed between the hydrogen ion and the added water whose 
speed is much lower than that of the normal hydrogen ion in alcohol. 
In the case of the weak acids, the addition of water increases the ioniza- 
tion, owing to the formation of a complex between water and the acid. 

The formation of a more or less definite complex between an acid 
and water is moreover indicated by the large energy change accompany- 
ing the solution of acids in water. It has been suggested that the hydro- 
gen ion is indeed an oxonium ion, bearing the same relation to oxygen 
that the ammonium ion does to nitrogen. The hydrogen ion would there- 
fore be OH3+- That the oxygen compounds form salt-like substances 
with the halogen acids is further borne out by the fact that oxygen com- 
pounds dissolved in the liquid halogen acids almost invariably yield 
electrolytic solutions, some of which are ionized almost as much as the . 
typical salts.^ At the same time it has been shown that the organic 

= Archibald, Journal d? Chimie physique, 11, 741 (1913). 



206 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

substance is associated with the cation.* In the case of sulphur, which 
element is closely related to oxygen, salts of the type R3SX are well 
known. 

Correspondingly, the ammonium salts dissolved in liquid ammonia 
exhibit all the properties of acids, and the ammonium ion exhibits the 
properties characteristic of the hydrogen ion.° If this conception regard- 
ing the nature of the hydrogen ion is correct, we should expect solutions 
of the acids in solvents, which do not possess the power of forming com- 
plexes of the type R3O+, to be relatively poor conductors. Such indeed 
appears to be the case. Dissolved in the alcohols, hydrogen chloride 
conducts fairly well; while dissolved in acetone,^ hydrogen chloride 
yields a solution of very low conducting power. In view of the fairly 
high dielectric constant of acetone, it is difficult to account for this be- 
havior of the acid except on the assumption that in this case there is 
little tendency to form the oxonium complex. There are no data to indi- 
cate that hydrogen chloride is a conductor when dissolved in sulphur 
dioxide or any other solvent which does not contain oxygen, nitrogen or 
other atoms capable of forming complexes. 

These various facts indicate that the hydrogen ion in water is, in 
fact, not a hydrogen ion, but an oxonium ion. Whether the charge is 
associated with the hydrogen or with the oxygen atom cannot be deter- 
mined in this case any more than it can in that of the similar ammonium 
salts. It appears likely, however, that in salts of this type the charge 
is associated either with the oxygen or nitrogen atom, or with the group 
as a whole, rather than with one of the hydrogen atoms. 

5. Ions of Abnormally High Conductance. Certain writers have 
sought to relate the abnormally high conductance of the hydrogen and 
hydroxyl ions with the fact that these ions are products of the ionization 
of the solvent itself.' They have therefore adopted a theory founded 
upon the old theory of Grotthuss,* according to which the mechanism of 
the conduction process consists, not in a transfer of the ions through the 
solution, but in an ordered arrangement of the polar molecules of the 
electrolyte, alternately positive and negative, in accordance with the im- 
pressed field. An interchange of positive and negative carriers takes 
place between adjacent molecules resulting thus in a separation of the 
products at the two electrodes. The work of Faraday and Hittorf has 
definitely overthrown the theory of Grotthuss, but these later writers 

♦Steele, Mcintosh and Archibald, Ztschr. ]. phys. Chem. SS, 176 (1906) 
r,, ' ^^r^'i.o" o,''??nio^''"?^ Am CJwm. J SS, 304 (1000); Franklin and Stafford, Am. 
Oliem. J. 28, 83 (1902) ; Franklin, Am. Chem. J. J,T, 285 (1912) 

' Lucasse, Thesis, Clark Univ., 1920. 
7i B "^nem^ ^ilf^lwil)^^"*^'"'^' ^^' ^^^ (1905); Hantzsch and Caldwell, Ztachr. }. 

'"Ann. h. Chhn. 58, 54 ('l806). 



CARRIERS IN ELECTROLYTIC SOLUTIONS 207 

assume that, in the case of the hydrogen and the hydroxyl ions in water, 
an interchange takes place between the ions and the solvent molecules 
with the result that the mean path over which these ions travel is reduced 
in proportion to the effective diameter of the solvent molecules which are 
concerned in the interchange. A priori, there is nothing to indicate that 
this hypothesis may not be correct. If it is correct, however, it must 
lead to certain definite consequences which we may now examine. 

In the first place, it is to be expected that a similar phenomenon will 
be found in solutions in non-aqueous solvents which are capable of 
furnishing ions. In the case of liquid ammonia an equilibrium exists of 
the type: 

or, perhaps, 

2NH3 = NH,- + NH/, 

where NH/ is the ammonium ion and NH^- is the basic ion of liquid 
ammonia. That such an equilibrium exists, is indicated by the fact that 
certain ammonolytic equilibria exist in ammonia solutions comparable in 
all respects with hydrolytic equilibria in aqueous solutions." On the 
basis of the above hypothesis, we should expect that the ammonium ions 
and the NH2" ions would exhibit an exceptionally high conducting power 
in liquid ammonia solutions. As may be seen by referring to the table 
of ionic conductances in Chapter II, the amide ion in liquid ammonia 
possesses a conducting power markedly lower than that of typical nega- 
tive ions, while the conductance of the ammonium ion is distinctly lower 
than that of the potassium ion. It follows, therefore, that in ammonia 
solutions the ammonium and the amide ions are in no wise exceptional. 
It has been maintained that the conductance of the alcoholate ion in the 
alcohols is abnormally high. According to the best data available, how- 
ever, the conductance of the alcoholates in alcohol ^° is of the same order 
as that of typical salts in these solvents. 

As a result of conductance and transference measurements with the 
formates in formic acid it has been shown that the formate ion in formic 
acid possesses an exceptionally high conducting power. While the pre- 
cise values are somewhat uncertain, roughly, the ionic conductances of 
the sodium, potassium and formate ions in formic acid at 25° are 14.6, 
17.5 and 51.6.^^ The limiting value of the conductance of hydrochloric 
acid in formic acid is approximately 75, compared with the value 69.4 ^^ 

•Franklin, J. Am. Chem. Soc. Br, 820 (1905). 

'"Robertson and Acree, Intern. Oongr. Appd. Chem. [S] 2ff, 609 (1912). 

" Schlesinger and Bunting, J. Am. Chem. Soc. J,l, 1934 (1919). 

" SchJesinger and Martin, J. Am. Chem. Soc. 36, 1618 (1914). 



208 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

for potassium formate, for example. Since the transference number of 
hydrochloric acid in formic acid is not known, it is uncertain whether 
or not the hydrogen ion in formic acid possesses an abnormally high 
conducting power. The evidence, however, indicates that the chloride 
ion possesses a conducting power not greatly smaller than that of the 
formate or hydrogen ion. The limiting value of the conductance of 
ammonium chloride can scarcely be lower than 52." The value is some- 
what uncertain because of the solvolytic reaction between the salt and 
the solvent. However, assuming probable values for the ionization con- 
stants of ammonium formate and hydrochloric acid and pure formic acid, 
it can be shown that the fraction of salt transformed to acid and base 
by reaction with the solvent cannot affect the conductance by more than 
a few units. If we assume, therefore, the value 52 for the limiting value 
of the equivalent conductance of ammonium chloride, and assuming for 
the conductance of the ammonium ion the value 18.8, which follows from 
the value 70.4 for the limiting value of the equivalent conductance of 
ammonium formate, we obtain for the limiting value of the conductance 
of the chloride ion the value 33.2 and for the hydrogen ion 42.8. This 
indicates that the conductance of the hydrogen ion in formic acid does 
not differ greatly from that of the chloride ion in the same solvent. The 
exceptionally high value found for the conductance of the hydrogen and 
the formate ions, like that of the chloride ion, is presumably due to the 
relatively smaller dimensions of these ions compared with those of the 
positive ions in formic acid. 

It has also been suggested that the pyridonium ion, CeHgNH*, pos- 
sesses an abnormally high conducting power in pyridine.^* This, how- 
ever, rests upon a false accepted value for the conductance of typical 
salts in pyridine. The conductance of pyridine hydrochloride at a dilu- 
tion of 32 liters and 25° in pyridine has been found to be 27.4. The 
conductance of sodium iodide in pyridine at a dilution of 57.7 liters and 
18° is 23.6.^^ In general, at these concentrations, the conductance of 
solutions in pyridine changes but little with concentration. Conse- 
quently the conductance of sodium iodide in pyridine at 32 liters would 
differ but little from that at the lower concentration. On the other hand, 
the conductance at 18° is materially lower than at 25° because of the 
greater viscosity of the solution at the lower temperature. Assuming a 
viscosity correction of two per cent per degree the conductance of sodium 
iodide at 25° would be approximately 27.0. In other words, the con- 

" SchlesiDger and Calvert, J. Am. Chem. Soc. S3, 1924 (1911). 
" HaDtzscb and Caldwell, loo. cit. 

'» Ottiker, Dissertation, Lausanne (1907); Kraus and Bray, J. Am. Chem Soc 35 
1379 (1913), 



CARRIERS IN ELECTROLYTIC SOLUTIONS 209 

ductance of a typical salt in pyridine differs but little from that of a 
salt of the solvent itself. 

While, therefore, there are cases in which the ions common to the 
solvent exhibit an abnormally high conducting power, as they do in 
water at ordinary temperatures, there are other cases in which the con- 
ducting power of these ions is entirely normal. In this connection it is 
to be borne in mind that with rising temperature the speed of the hydro- 
gen and hydroxyl ions in water approaches that of the more slowly 
moving ions. At 306° the conductance of the hydrogen ion differs from 
that of the potassium ion less than the conductance of the potassium ion 
differs from that of the acetate ion at ordinary temperatures. As has 
been pointed out, the relative decrease in the speed of the more rapidly 
moving ions at higher temperatures is due to the increase in the size 
of the more rapidly moving ions. It seems more rational, therefore, to 
ascribe the abnormally high speed of the hydrogen and hydroxyl ions in 
water to the low value of their hydration, which moreover is in accord 
with the experimentally determined values of the relative hydration of 
the different ions in water at ordinary temperatures. 

While it cannot be definitely stated that all hydrogen ions in water 
are associated with at least one molecule of water, it nevertheless appears 
probable that such is the case. Were the hydrogen ion unhydrated, we 
should expect a much greater value for the conductance of the hydrogen 
ion. In the case of liquid ammonia solutions, it has been shown that the 
speed of the negative electron, which at low concentrations is associated 
with at least one ammonia molecule, is approximately seven times that of 
the sodium ion. It seems not unlikely that the negative electron in dilute 
solutions is actually associated with a greater number of ammonia mole- 
cules. Taking all these facts into consideration, it appears probable that 
the hydrogen ion is associated with at least one molecule of water. 

It is evident that our conception as to the nature of the ions has 
undergone a great amplification during the past twenty years. Prior to 
that time the ion of an element was looked upon merely as an atom of 
the element associated with a charge. Now, however, we know that the 
ions consist of more or less definite complexes containing the solvent, and 
the nature and dimensions of these complexes depend, not alone upon 
the properties of the electrolyte and of the solvent, but also upon the 
condition under which the solution exists, such as concentration, tempera- 
ture, pressure, etc. 

6. The Complex Metal- Ammonia Salts. A number of salts of the 
heavy metals, particularly those of cobalt, chromium and the platinum 
metals, form series of compounds with ammonia in which there appears 



210 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

a remarkable relationship between the number of ammonia molecules 
associated with the complex salt and the properties of the salt, both in 
solution and in a crystalline state. While the compounds containing 
ammonia, or ammonia derivatives, are, in general, the most stable repre- 
sentatives of this class, many other compounds are known where other 
molecules function in a manner similar to those of ammonia. These 
complex salts have been studied extensively by a number of investigators, 
notably by -Werner ,^^ who has proposed a theory of the constitution of 
these compounds which has met with remarkable success in accounting 
for their properties. It is not proposed to give here an extended exposi- 
tion of Werner's theory, since that is beyond the scope of this mono- 
graph. However, a brief outline may be given here, in order to make 
intelligible the relation between the constitution of the complex metal- 
ammonia salts and their ionic properties. 

According to Werner's theory, the strongly electronegative elements 
or groups of elements are attached to the nuclear atom by what are termed 
principal valences, while neutral groups of molecules such as ammonia are 
associated with the nuclear atom by auxiliary or secondary valences. A 
definite number of atoms or groups is always attached to the nuclear atom, 
either by principal or secondary valences, and this number, which is 
usually 6 and sometimes 4, is fixed. The number of atoms or groups so 
attached is called the co-ordination number. The charge on the nuclear 
complex depends upon the number of principal valences comprised within 
the co-ordination number. If N is the normal valence of the nuclear atom, 
C the co-ordination number of the nuclear group, and n the number of 
secondary valences satisfied in the nuclear group by neutral complexes, 
such as ammonia, etc., then the number -of charges on the nuclear group 
or complex is: q = N — C + n. Usually the co-ordination number is 
6 or 4. If, for example, the co-ordination number is 6 and the normal 
valence of the nuclear atom is 4, then, if n = 2, that is if two molecules 
are associated in the nuclear complex, g = 0, and the charge on the com- 
plex will be zero. If, on the other hand, n were 0, the charge on the 
nuclear complex would be — 2; that is, the nuclear complex would carry 
two negative charges. On the other hand, if n were 6, g = + 4; that is, 
the nuclear complex would carry 4 positive charges. For a co-ordination 
number 6, the maximum variation in the charge on the nuclear complex 
is from 4 positive to 2 negative charges. An example will serve to make 
the relationships clear. Platinum chloride, PtCl^, in which platinum 
appears with the principal valence of 4, forms with ammonia the follow- 
ing series of complexes, all of which are known except the second. 

"Werner, New Ideas on Inorganic Chemistry. Trans, by B. P. Hedley, 1911. 



CARRIERS IN ELECTROLYTIC SOLUTIONS 211 



1 2 

[Pt(NH3).lCU [PtgJ^H'^']ci3 


[Ptg?f3).]c.. 


[Ptg?5=)>]ci 


Kr'^1 


6 7 

[PtgHaJK [PtCl.]K, 


Chloride of 
Drechsel's Unknown 
base 


Platini- 

diammine 

chloride 


Platinimono- 

diaminine 

chloride 


Platini- 

diammine 

chloride 


Cossa's Potassium 

second platinum 

salt chloride 



Those elements or groups appearing with platinum within the brackets 
are contained in the nucleus, while those without the brackets 
carry charges and are capable of ionization. The co-ordination number 
of platinum in the nucleus is 6. The charge on the nucleus is therefore 
given by the equation g = 4 — 6 + n, where n is the number of ammonia 
molecules in the complex. In the first compound [PtlNHg) JCl^, n = 6 
and g ^ + 4. This compound therefore ionizes according to the equa- 
tion: [Pt(NH3)JCl,= [Pt(NH3),]^++^- + 4Cl-. On the other hand, in 
the compound [PtClJK^, n = and q = — 2. This compound, there- 
fore, ionizes according to the equation: [PtClelKj ^ PtCV' + 2K+. 
The manner in which the ionization takes place in the other compounds 
may obviously be derived from the equation given. If Werner's theory 
is correct, then, when the various compounds are dissolved in water, the 
conductance of the resulting solutions should vary in correspondence with 
the number of changes involved in the ionization reaction. At low con- 
centrations, the conductance of the first compound should lie in the 
neighborhood of 500; that of the third compound, in the neighborhood of 
200; that of the .fourth, in the neighborhood of 100; while that of the 
fifth should be zero. On the other hand, that of the sixth should lie in 
the neighborhood of 100 and that of the seventh in the neighborhood of 
200. In solutions of these last two compounds, the platinum complex 
should appear as anion. This' consequence of Werner's theory has been 
confirmed by experiment. The conductance of the first, third, fourth, 
fifth, sixth and seventh compounds at 0° and at a dilution of 1000 liters 
are respectively: 522.9, 228, 96.75, 0, 108.5, and 256. 

The conductance of the fifth compound is actually not quite zero, 
since in solution compounds of this type are not entirely stable and reac- 
tion takes place with the water, wherein molecules of water enter the 
nucleus and thus produce a charged complex, the water functioning in a 
manner similar to that of ammonia. However, in many cases values of 
A less than unity have been obtained, and it has been shown that the 
conductance is a function of the time and that, moreover, the reaction is 
catalyzed at the electrode surfaces.^'^'' 

There can be no doubt but that the ionization of the complex metal- 
ammonia and other similar salts depends upon the combination of am- 

i»a Werner and Herty, Ztschr. /. phys. Chem. 38, 331 (1001). 



212 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

monia with the nuclear atom. What characterizes these compounds in 
particular is their stability. Similar relations may exist in the case of 
other salts which show a pronounced tendency to form complexes, such as 
calcium salts for example, but in these cases reaction between the com- 
plex and the solvent medium takes place very rapidly. The behavior of 
these complexes in water does not differ greatly from that of calcium 
chloride in propyl alcohol, whose ionization is greatly increased on the 
addition of water. On the other hand, it is to be borne in mind that in 
non-aqueous solutions those salts which exhibit only a slight tendency to 
form complexes with water are highly ionized in all cases. This is 
particularly true, for example, of potassium salts. It appears probable 
that such salts do not form complexes similar to the metal-ammonia 
salts. It is probable, however, as we have seen, that all ions are hydrated. 
It appears likely that the solvent molecules may be associated with the 
ions in several ways. Certain of the solvent molecules may be combined 
in a more or less definite manner, as in the metal-ammonia complexes, 
while other molecules may be associated with the ions due to the opera- 
tion of purely electrical forces. 

7. Positive Ions of Organic Bases. With the exception of ions of 
salts of organic bases and a few salts of the type of the ammonium salts, 
the positive ions consist essentially of metallic elements. This tendency 
of the metallic elements to form electropositive ions is in harmony with 
prevailing conceptions regarding atomic structure. The organic bases 
are derived from the less electropositive elements on the introduction of 
organic radicals, such as alkyl and aryl radicals, into combination with 
the nuclear element. The number of carbon radicals introduced depends 
upon the valence of the element in question, and upon its position in the 
periodic system. For elements up to the fifth group, the organic bases 
have the constitution: R^_^M"X, where n is the maximum valence of the 
element with respect to negative elements. For elements of the fifth to 
the seventh groups, inclusive, the bases have the constitution: R , ^M^X 

where n is the valence of the element toward hydrogen. Thus, we have 
the organic bases: CHsHgOH, (CH3)2T10H, (CH3)3SnOH, (CH3),N0H, 
(0113)38011 and (CeH6)2lOH. The strength of the organic bases de- 
pends upon their constitution. As hydrogen is substituted by organic 
groups, particularly alkyl groups, the strength of the base in general 
increases, although a marked increase does not take place until the sub- 
stitution of the last hydrogen atom occurs, in which case the resulting 
base exhibits a maximum strength. Thus, monomethyl-, dimethyl- and 
trimethylammonium hydroxides are comparatively weak bases, while 



CARRIERS IN ELECTROLYTIC SOLUTIONS 213 

tetramethylammonium hydroxide is a base whose strength is practically 
the same as that of potassium hydroxide. The positive ions of the strong 
organic bases possess distinct metallic characteristics in their compounds. 
With a few exceptions, these ionic groups may not be obtained in a free 
neutral state, since in this condition they are comparatively unstable, 
yielding, as a rule, various neutral organic compounds. The tetramethyl- 
ammonium group, as indeed the ammonium group itself, possesses an 
appreciable stability. So, for example, the ammonium group forms an 
amalgam in which the presence of the free ammonium group has been 
established." The tetramethylammonium group forms a stable, solid, 
metallic amalgam with mercury ,^8 and this group, moreover, may be pre- 
cipitated in a free state by electrolysis in ammonia solution." Under 
these conditions the free group dissolves in ammonia to form a solution 
which resembles solutions of the alkali metals in the same solvent. These 
solutions, however, are relatively unstable so that their properties have 
not been further investigated. 

The mercury group, CHgHg, has been obtained in a free state by elec- 
trolytic precipitation from an ammonia solution.^" The free group is a 
distinctly metallic substance which is a good conductor of the electric 
current. This group, while relatively stable in comparison with other 
groups, nevertheless reacts slowly, even at low temperatures, and at high 
temperatures it reacts instantaneously according to the equation: 

2CH3Hg = Hg + Hg(CH3),. 

Not only do the ions of the organic bases, therefore, resemble the metallic 
elements, but the free basic groups themselves, when they possess suffi- 
cient stability to admit of their being isolated, exhibit metallic properties. 
The metallic state of a substance is not one characteristic merely of ele- 
ments which themselves are metallic in the elementary condition, but 
includes likewise various groups of elements whose constitution is such 
that they carry a negative electron which is relatively loosely attached to 
the group. 

8. Complex Anions. Our knowledge of the structure of anion com- 
plexes is comparatively limited. No data are so far available which 
definitely establish that the anions in water are hydrated. It is true, 
that, from the conductance values of the anions and the hydration values 
of the cations, it may be inferred that the anions are likewise hydrated, 
but the hydration of the anions has not been experimentally verified. 

" Coehn, Ztschr. f. Anorg. Ohem. S5, 430 (1900). 
"McCoy and Moore, J. Am. Chem. Soc. SS, 273 (1911). 

'» Palmaer, Ztschr. g. Electroch. 8, 729 (1902) ; Kraus, /. Am. Otiem. Soc. 35, 1732 
(1913). 

"> Kraus, loc. cit. 



214 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

The existence of definite anion-complexes comparable, for example, 
with those of the cobalt and chromium salts is not indicated by the proper- 
ties of electrolytes, either in solution or in the solid and liquid state. The 
anions often consist of definite groups containing one or more electro- 
negative atoms. Among these we have, for example, the nitrates, chlo- 
rates, sulphates and other common anions, as well as many anions of 
organic acids. So far as the degree of ionization is concerned, salts of 
compound anions exhibit properties similar to those of salts of simple 
anions. The ionization of the hydrogen derivatives, namely the acids, 
of such anions, however, is largely dependent upon the nature of the 
atoms occurring in the anion complex. The introduction of strongly 
electronegative elements into the anion complex increases the strength, 
that is, the ionization of the acid. This behavior of the acids is so well 
known that details need not be introduced here. 

Certain elementary ions form complex anions with the same or other 
elements, a more or less complex equilibrium existing among the various 
complex anions formed in solution. The most common example of a 
complex anion of this type is the complex iodide ion which is formed 
by the direct interaction of the iodide ion with iodine, forming the ion 
I-.I2. The equilibrium in the case of the tri-iodide ion has been exten- 
sively studied by a number of investigators. The mean composition of 
the solution in such cases depends upon the concentration, since the 
equilibrium between the simple and the complex ion is a function of the 
concentration.^^ 

It is well known that the halogen salts form various complexes with 
other halogens, thus indicating that complex anions are formed between 
a halogen ion of one element with other elements of the halogen group. 
The chlor-iodides are familiar examples of this type. The equilibrium 
in the case of these complex anions has not been extensively studied. 

The work of Kiister ^^ indicates that the normal sulphide ion reacts 
with excess sulphur to form a series of complex sulphur anions. These 
anions appear to be comparable with the complex iodide ion, the charge 
being associated with the original sulphide anion. The mean composition 
of a solution of sodium sulphide in equilibrium with free sulphur varies 
as a function of the concentration. The problem in the case of aqueous 
solutions is complicated owing to hydrolysis. The behavior of aqueous 
solutions of the alkali selenides and tellurides indicates that these metals 
also form complex anions in the presence of excess of these metals.^^ 
They have not, however, been extensively investigated. 

"Bray and MacKay, J. Am. Ohem. 80c. S2, 915 (1910). 

""Kflster and Heberleln, Zteohr. f. Anorg. Ohem. J,S, 53 (1905) ; Kiister, ibii., iS. 481 
(1905). "Tibbals, J. Am. Ohem. 800. SI, 902 (1909). 



CARRIERS IN ELECTROLYTIC SOLUTIONS 215 

Solutions of complex selenides and tellurides have been obtained in 
liquid ammonia by the action of the normal salts on the free elements." 
Solutions of the complex tellurides in liquid ammonia are the only ones 
which so far have been extensively investigated. The normal telluride, 
which is only slightly soluble in ammonia, is formed by the direct action 
of the metal on sodium in ammonia solution. The telluride so formed 
IS a white substance, apparently somewhat crystalline in character. In 
the presence of excess tellurium the normal telluride reacts with the metal, 
forming a complex tellurium salt which is very soluble in ammonia. The 
composition of the solution in equilibrium with a normal telluride NagTc 
is NajTej.^'^ Apparently the following reaction takes place: 

N^^Te g^^ii^ + Te gQii^i = Na.Te, solution- 

This solution exhibits an intense violet blue- color. When the normal 
telluride NajTe has disappeared, the complex NajTea in solution reacts 
with free tellurium to form another complex. In concentrated solutions 
the composition of the ammonia solution corresponds very nearly with 
NagTe^. The exact value of the composition, however, is a function of 
the concentration, the amount of tellurium in solution decreasing at lower 
concentrations.^^ The color of the solution in equilibrium with metallic 
tellurium is deep red. 

The molecular weight of the telluride in equilibrium with metallic 
tellurium has been determined and found to correspond with the formula 
NajTe.Tex; that is, sodium is associated with a divalent complex tel- 
lurium anion.^' 

While the normal telluride is a white substance exhibiting only non- 
metallic characteristics, the product resulting on evaporating a solution 
containing larger amounts of tellurium is metallic in appearance, indicat- 
ing that the salts of the complex tellurides are metallic substances. This 
behavior of the complex tellurides in the free state is particularly im- 
portant when we come to consider similar complex anions of metals of 
the fourth and fifth groups. 

Whereas our knowledge of the complex anions of this type has pre- 
viously been restricted chiefly to elements of the sixth and seventh 
groups, in recent years, through a study of solutions in liquid ammonia, 
evidence has come to light which indicates that the elements of the 
fourth and fifth groups form complex anions similar in character to the 
complex sulphide and iodide ions. In the case of the salts of these com- 

"Hugot Compt. rend., 1^9, 299 and 388 (1899). 
"■Chiu, Dissertation, Claris University (1920). 
""B.K. Chiu, loc. cit. ., ^„„^, 

='E. H. Zeitfuebs, Dissertation, Clark University (1921). 



216 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

plex anions, however, the non-metallic characteristics have disappeared, 
and these substances in the solid state are metals. In solution, how- 
ever, they exhibit properties similar to those of tellurium. A charac- 
teristic property of such solutions is the existence of anions of distinctly 
metallic elements. Thus, lead is precipitated on the anode when the 
current is passed through a solution containing the complex Na^Pb-Pb^.^* 
A similar result has been obtained in the case of the antimony complex 
NasSb.Sbx.^^ In a solution of the lead complex in equilibrium with lead, 
2.25 atoms of lead are precipitated on the anode per equivalent of elec- 
tricity.'" This corresponds with the mean composition of the solution. 
The proportion of lead to sodium in the presence of excess lead is inde- 
pendent of the concentration of the solution. In the case of the anti- 
mony complex, the mean composition of the solution is a function of 
the concentration. The maximum lies in the neighborhood of 0.4 N 
sodium.'^ At lower concentrations, the mean composition falls off 
sharply from the value 2.33 at the maximum to 1.2 at a concentration of 
0.005 N. Bismuth and tin likewise form complexes of a similar nature 
which have not thus far been studied in detail. 

The solutions of these complexes, except possibly at the highest con- 
centrations, are purely electrolytic in character.'^ While the number of 
charges associated with the negative complex has not been definitely 
determined in the case of lead and antimony, it is probable that the 
charges are respectively 4 and 3, corresponding with the position of these 
elements in the periodic system. It is evident that many metallic ele- 
ments are capable of forming complex anions similar to the complex 
sulphur and iodide ions. The compounds which are left behind on 
evaporation of ammonia are metallic. In view of the electrolytic prop- 
erties of these compounds when in solution, it appears probable that the 
solid compounds themselves are, in fact, salt-like in character, the more 
electronegative element carrying a negative charge. The existence of a 
large number of compounds in binary systems, such as those of sodium- 
and lead, is probably due to the formation of negative ionic complexes. 
In all likelihood, this property is not confined to the metals whose com- 
pounds are soluble in ammonia. It is probable that the constitution of 
the compounds formed between the strongly electropositive elements and 
such elements as thallium and mercury is similar to those of lead. 

9. Other Complex Ions. Complex anions are formed by many salts 
of metallic and non-metallic elements on interaction with salts of the 

»Kraus, /. Am. Chem. Soc. 29, 1557 (1907) ; Smyth. iUd S9 1299 n9iqi 

"Peck, J. Am. Chem. Soc. 40, 335 (1918). ' ' U919). 

"Smyth, loo. cit. 

"Peck, loc. cit. 

"Kraus, J. Am. Chem. Soc. |3, 752 (1921). 



CARRIERS IN ELECTROLYTIC SOLUTIONS 217 

more electropositive elements. Many such complex anions have been 
investigated in which mercury, tin, lead, platinum, silicon and other ele- 
ments appear in the anion complex in association with strongly electro- 
negative elements such as chlorine, fluorine, etc. The constitution of 
these complex anions is accounted for by Werner's theory which has 
already been briefly outlined. 

Complex or, preferably, intermediate ions, both positive and negative, 
may be formed when salts of higher type ionize in stages. Such ions 
have many representatives among the higher types of weak acids and 
bases when the ionization constants of the different ions have different 
values. This is the case, for example, with phosphoric acid. 

Whether similar complex ions are commonly formed in solutions of 
salts of higher type is uncertain. The cation transference number of 
cadmium iodide at high concentrations is greater than unity, which 
clearly indicates the existence of an intermediate cadmium ion. In the 
case of other salts, the existence of intermediate ions is not definitely 
established although, as we shall see below, the existence of such ions in 
mixtures may be inferred from solubility data. There are no data 
available relative to the existence of similar ions in non-aqueous solu- 
tions. It is possible, also, that binary electrolytes may associate and 
dissociate with the formation of complex ions. Their existence has not 
been established. 



Chapter IX. 
Homogeneous Ionic Equilibria. 

1. Equilibria in Mixtures of Electrolytes. If the constituents in a 
mixture of two or more electrolytes obey the mass-action law, then the 
equilibrium in the mixture may at once be determined if the values of 
the mass-action constants are known. The values of these constants 
may in general be determined from a study of solutions of the pure 
substances under corresponding conditions. The equations underlying 
such equilibria have the form: 

TS —^> 

where C* denotes the concentration of the positive ions, C~ that of the 
negative ions, and C^ that of the un-ionized fraction of a given elec- 
trolyte. K is the ionization constant of the electrolyte in question. For 
every electrolyte appearing in the solution as an un-ionized molecule, 
the concentrations of its un-ionized fraction and of- its ions appear as 
variables. In general, these ions will also be common to other electro- 
lytes present in the mixture. The total number of ionic species in solu- 
tion will be equal to the total number of un-ionized species in solution 
in case any number of electrolytes without a common ion are mixed. 
The mass-action law leads to a series of reaction equations of the type: 

Ml- X X,- = Z,M,X„ 

and the concentrations of the various molecular species present in the 
solution, and to a series of condition equations of the type: 

M,X, + M,X, + . . . + M,- = C j^^ 
and MiXi + M^Xi-f ... +Xi- = Cy ^ 

The number of equations will always be equal to the number of variables 
and the concentrations of the various molecular species present in the 
solution may be determined by solving the resulting simultaneous equa- 
tions. If two electrolytes without an ion in common are mixed, the 
resulting reaction equations are: 

218 



HOMOGENEOUS IONIC EQUILIBRIA 219 

M/ X X^- = K,M,X, 
M/ X Xf = ^3M,Xi 
M,- X X,- = KMiX,, 
and the condition equations are: 

M, + M,X, + M,X, = C, 
M, + M,X, + M,X, = C, 
X, + M,X, + M,X, = C, 
X, + M,X, + M3X, = C, 

where C^ and C^ are the total concentrations of the base M^ or acid Xj, 
which are necessarily equivalent, and the base M^ or the acid X^, which 
are likewise equivalent. From these eight equations the concentrations 
of the eight different molecular species may be determined for any con- 
centrations Cj and C2 of the total acids and the total bases in solution. 
In this case, interaction with the solvent is assumed not to take place. 
In a mixture of two electrolytes with a common ion we have the reaction 
equations : 

M/ X X- = K,M,X 

M^- X X- == K.M^X 

and the condition equations: 

M,X + Ml = C, 
M,X + M, = C^ 

M^X + M,X + X = Ci + C3. 

In this case the solution of the problem is comparatively simple. 

In a mixture of two electrolytes having an ion in common, assuming 
the mass-action law to hold, the ionization of the electrolytes in the mix- 
ture will be the same as that in the original solutions before mixing, if 
the concentrations of the common ion in these solutions, before mixing, 
are equal. Such solutions are said to be isohydric.^ This result is a 
consequence of the law of mass-action. Let M^*, M.^* and X" be the 
concentrations of two solutions having in common the ion X". It is 
obvious that the concentration of the common ion in these two solutions 
will be equal to M^- for the first solution and M2+ for the second solution. 
Let a volume Vj liters of the first solution be mixed with a volume of Y^ 
liters of the second solution. If the concentrations of the ion X" in the 
two original solutions are equal, then we obviously have: 

Ml* = M/ — X-. 

1 Arrhenius, Ann. d. Phys. 30, 51 (1887) ; Ztschr. f. phys. Chem. 2^84 (1888) ; ibid., 
5, 1 (1890). 



220 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In the mixture, therefore, assuming that no displacement of the equi- 
librium takes place, we should have for the concentration of the ions M^* 

the value ^, ^, \\ , for that of the common ion ^y , y and tor 

that of the un-ionized fraction M,X, y^^^y^ . If the law of mass-action 
holds, we have the equation: 

-y —IS-i. 

M.X.y-J^y- 

If Mi+ = M/, the expression for the concentration of the common ion 
becomes: 

and the equilibrium equation reduces to: 

M,- X X,- 



M,X, 



K,. 



In other words, if the concentration of the common ion is the same in the 
original solutions, then, if these solutions are mixed in any proportion, 
assuming no change in the equilibrium to take place, the concentrations 
of the ions in the mixture will be such as to fulfill the conditions necessary 
for equilibrium. 

The correctness of this principle may readily be tested in the case of 
weak acids. Since the conductance in solutions of the acids is due chiefly 
to the conductance of the hydrogen ion, it follows that two acids will 
have the same concentration of the hydrogen ion when the solutions 
have the same specific conductance. Therefore, a mixture of two solu- 
tions fulfilling these conditions will have the same specific conductance 
as the original solutions. If the anions have different conductance 
values, the specific conductance of isohydric solutions will differ in 
proportion to the conductance of these anions, and the specific conduct- 
ance of a mixture of the solutions will be the arithmetic mean of that 
of the components. This principle has been extensively tested by the 
conductance as well as other methods and has been shown to hold true 
for mixtures of weak acids and bases. 

It has been found, however, that even in solutions which do not con- 
form to the law of mass-action, that is, in solutions of strong electrolytes, 



HOMOGENEOUS IONIC EQUILIBRIA 221 

a similar condition holds. If, for example, solutions of sodium chloride 
and potassium chloride have the same ion concentration, then, on mixing, 
the concentration of the ions in the mixture will be the same as that in 
the original solutions. Apparently, then, the isohydric principle holds, 
even in the case of electrolytes which do not obey the law of mass-action. 
This principle has been employed very extensively for the purpose of 
calculating the concentrations in mixtures of strong electrolytes. If the 
electrolytes in a given mixture do not obey the law of mass-action, then 
it is obviously impossible to calculate the equilibrium in the mixture 
unless we know the law governing this equilibrium. The isohydric prin- 
ciple is an empirical relation which has been assumed to govern the 
equilibrium in mixtures. In order to test the correctness of this prin- 
ciple, it is obviously necessary to determine the concentrations of the 
ions in the mixture by some independent means. 

The law of equilibrium for a given electrolyte in a mixture must 
reduce in the limit to that of a solution of the electrolyte in the pure 
solvent. It has been shown that, for a strong electrolyte, Equation 11 
holds very nearly. According to this equation, the ratio of the product 
of the concentrations of the ions divided by the concentration of the 
un-ionized fraction varies as an exponential function of the ion concen- 
tration. It is clear that this relation conforms to the principle of iso- 
hydric solutions. In a mixture of electrolytes, the equation might take 
the form: 

P. 

(50) ^=D{^Uir+K, 

u 

where P- is the value of the ion product, C^ is the concentration of the 
un-ionized fraction, and C^ is the total concentration of the positive or 
negative ions in the mixture. Indeed, it is apparent that an equation 
of the form: 

(51) ^=F{^C^) 

u 

will conform to the isohydric principle,^ where P(2C^) is any explicit 
function of the total ion concentration of the mixture. For, on mixing 
two solutions whose ion concentrations are C( and Cj", the equilibrium 
will be unaffected by the relative volumes of the solutions mixed, pro- 

•Arrhenius, Ztschr. f. phys. Chem. SI, 218 (1899). 



222 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

vided that C/ and C-" are equal. Equation 51, therefore, is the analyti- 

cal expression of the isohydric principle. In the limit, as the second com- 
ponent in the mixture disappears, the equation reduces to that for the 
first salt alone. In the case of mixtures of electrolytes without a com- 
mon ion the same expression applies. 

Equation 51 is not the only function which might be assumed to hold 
for the mixture which reduces to the form of Equation 11 in the case 
of a solution of a single electrolyte. We might assume for the mixtures 
a function of the form: 

(52) -^=F{P.), 

u 

where again P- is the ion product. In the limit the concentrations of 

the positive and negative ions become equal for the solution of a single 
salt, and consequently this equation reduces to the form of Equation 11. 
The isohydric principle, or more generally, the iso-ionic principle, is a 
consequence of the law of mass-action, but, when the law of mass-action 
fails to hold, there is no reason for assuming that Equation 51 rather 
than Equation 52 is correct, for both reduce to the same limiting form 
in the case of a solution of a single electrolyte. We may, therefore, 
inquire which of the two functions corresponds most nearly with the 
experimental values. 

In order to test the functions in the case of mixtures, it is obviously 
necessary to measure some property of these mixtures by independent 
means, as, for example, the conductance of a mixture of electrolytes. 
Assuming that the conductance of the ions in the mixture is the same as 
that of the same ions in pure solutions, it is possible to calculate the 
specific conductance of the mixture, if the form of the conductance func- 
tion for the pure electrolytes is known, and if a function is assumed for 
the mixture. If the assumed function is correct, then the calculated 
specific conductance for the mixture should correspond to the measured 
specific conductance of the mixture within the limits of experimental 
error. If the calculated and observed values do not correspond, it fol- 
lows that the function assumed for the mixture is not correct. That an 
equilibrium actually exists. in the mixture appears to be beyond question, 
although the exact nature of the reaction may be somewhat in doubt. 

Bray and Hunt ' have measured the specific conductance of mixtures 

of sodium chloride and hydrochloric acid in water at 25°. They have 

• likewise calculated the specific conductance of the mixtures, assuming 

"Bray and Hunt, J. Am. Chem. Soc. S3, 781 (1911). 



HOMOGENEOUS IONIC EQUILIBRIA 



223 



the isohydric principle; that is, assuming Equation 51. The results are 
given in Table LXXXIII, in which the concentrations of sodium chloride 
and hydrochloric acid are given in the second and third columns re- 
spectively, and the measured specific conductance is given in the fourth 
column. In the fifth column is given the specific conductance calculated 
on the assumption of the isp-ionic principle, namely Equation 51, while in 
the seventh column is given the value of the calculated specific conduct- 
ance, assuming Equation 52. In the sixth and eighth columns are given 
the percentage deviations between the measured and calculated values. 

TABLE LXXXIII. 

Measured Specific Conductance of Mixtures of NaCl and HCl Com- 
PABED WITH Values Calculated According to Equations 51 and 52. 





Concentration 




Specifi 


c Conductance n 






(Approx.) 


Calculated 












millimols 




Equa- 




Calculated 




No. 


NaCl 


HCl 


Measured 


tion 51 


% Dif. 


Equation 52 


% Dif. 


1 


100 


100 


47.25 


48.21 


— 2.1 




47.09 


+ 0.3 


2 


100 


50 


29.14 


29.62 


— 1.6 




28.82 


+ 1.1 


3 


100 


20 


18.06 


18.31 


— 1.4 




17.84 


+ 1.2 


4 


100 


10 


14.36 


14.50 


— 1.0 




14.18 


+ 1.2 


5 


100 


5 


12.52 


12.59 


— 0.6 




12.39 


+ 1.1 


6 


100 


2 


11.41 


11.45 

Mean 


— 0.3 


% 


11.35 

Mear 


+ 0.5 




— 1.15 


I + 0.85% 


7 


20 


50 


21.75 


21.89 


— 0.7 




21.65 


+ 0.4 


8 


20 


20 


10.157 


10.27 


— 1.1 




10.13 


+ 0.3 


9 


20 


10 


6.253 


6.307 


— 0.9 




6.221 


+ 0.5 


10 


20 


4 


3.889 


3.919 


— 0.8 




3.870 


+ 0.3 


11 


20 


2 


3.101 


3.118 


— 0.6 




3.094 


+ 0.2 


12 


20 


1 


2.709 


2.721 

Mean 


— 0.4 


% 


2.702 

Mear 


+ 0.3 




— 0.75 


1 + 023% 


13 


5 


12.5 


5.651 


5.678 


— 0.5 




5.646 


+ 0.1 


14 


5 


5 


2.632 


2.650 


— 0.7 




2.634 


— 0.1 


15 


5 


2 


1.621 


1.630 


— 0.6 




1.619 


+ 0.1 


16 


5 


1 


1.011 


1.016 

Mean 


— 0.5 


% 


1.010 

Meal 


+ 0.1 




— 0.57 


1 + 0.05% 



Comparing the measured values of the specific conductance with those 
calculated on the basis of Equation 51, it is seen that the deviations from 
the iso-ionic principle are consistently larger than any conceivable experi- 
mental error. In the case of 0.1 normal solutions of sodium chloride, the 



224 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

mean error is 1.15 per cent; for 0.02 normal solutions, 0.75 per cent; 
and for 0.005 normal sodium chloride solutions, the mean deviation is 
0.57 per cent. At the lower concentrations the agreement is measurably- 
better than at the higher concentrations, a result which is perhaps not' 
unexpected, since at concentrations as high as 0.1 normal viscosity effects 
unquestionably come into play. The agreement between the measured 
and calculated values based on Equation 52 is markedly better than that 
of values based on Equation 51. In the case of the 0.1 normal solutions of 
sodium chloride, the mean deviation is 0.85 per cent. In the mixtures 
of sodium chloride of concentration 0.02 and 0.005, the mean deviations 
are respectively 0.33 and 0.05 per cent, values which fall very nearly 
within the limits of experimental error. In calculating the specific con- 
ductances of the mixtures according to Equation 52, 424 was assumed 
for the value of Ao for hydrochloric acid and 127 for that of sodium 
chloride. These values may be somewhat in error, but it is to be noted 
that the calculated specific conductances are affected to only a very 
small extent by the value assumed for Ao. It must be concluded from 
these results that the isohydric principle is not applicable to mixtures 
of strong electrolytes. In the case of the mixtures of hydrochloric acid 
and sodium chloride, at any rate. Equation 52 yields results which corre- 
spond quite closely with the observed values at low concentrations. It 
is uncertain, however, that a similar correspondence will be found in the 
case of mixtures of other electrolytes. Eor the present, therefore, the 
form of the function which should be assumed in the case of mixtures of 
strong electrolytes remains doubtful. 

2. Hydrolytic Equilibria. Water itself is ionized to a slight extent 
into hydrogen and hydroxyl ions. There therefore exists in water an 
equilibrium which, if the law of mass-action holds, is expressed by the 
equation: 

H^XOH- = li:^, 

where Z^ is the ionization constant of water. The concentration of the 
hydrogen and hydroxyl ions in pure water has been determined by 
Kohlrausch from the conductance of very pure water. At 18° this method 
yielded the value 0.80 X 10-' for the concentration of the hydrogen and 
hydroxyl ions in pure water. The ionization constant has also been 
determined from the electromotive force of gas cells, from the rate of 
certain esterrification reactions and from the hydrolysis of certain salts 
in water. In these latter methods, an electrolyte has, in general, been 
present, which naturally introduces an uncertainty as to the effect of 





1.1 




1.2 


0.8 




... 


1.19 


0.80 


1.06 


0.68 


0.91 



HOMOGENEOUS IONIC EQUILIBRIA 225 

the electrolyte on the ionization constant of water. The results of the 
various methods are summarized in the following table. 

TABLE LXXXIV. 

The Hydrogen-Ion Concentration (X IC) in Pure Water as Deter- 
mined BY Various Investigators. 

Investigator Method of Determination 0° 18° 25° 

Arrhenius Hydrolysis of sodium acetate by 

ester-saponification 

Wijs Catalysis of ester by pure water 

Nernst Electromotive force of gas cell 

Lowenherz Electromotive force of gas cell 

Kohlrausch and 

Heydweiller . . Conductance of pure water 0.36 

Kanolt Hydrolysis 0.30 

When a salt is dissolved in water, interaction takes place between 
the ions of the salt and the ions of water with the resultant formation 
of un-ionized molecules of acid, or of base or of both, depending upon 
the strength of the acid and the base. Assuming the law of mass-action 
to hold in the mixture for both acid and base, and assuming that the 
salt is highly ionized and that its ionization function is known and is 
the same in the mixture as it is in a solution of the salt alone, the con- 
centration of the various constituents in the mixture may be obtained 
from a solution of the reaction equations: 

H- X X- = KJiX, 

(53) M* X OH- = K^MOU, 

H- X OH- = K^, 

and the condition equations: 

MX -f HX 4- X- = C^, 

(54) MX 4- MOH + M^ = C^, 
M^ -f H- = X- -f 0H-, 

where K , Kj^ and K are the ionization constants of acid, base, and 

water, respectively, and C and C^ are the total concentrations of acid 

and of base, and the other symbols represent the concentrations of the 
various constituents concerned in the reaction. Let us assume that the 
acid is stronger than the base, in which case H+ is greater than 0H-. 
Let Y represent the fraction of base present in the form of ions. Since 



226 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

M* differs from X", Ys is not identical with the ionization of the salt, 
but, unless the hydrolysis is great, the value of y^ will not differ appre- 
ciably from that of the salt at the concentration in question. . Let h 
represent the total fraction of base present in the un-ionized condition, 
in which case h is the hydrolysis coefficient. A solution of the above 
equations leads to the equation: 



(55) 



^«,Ts(i-/*)r _ . _ K,ys(^-h) Kj^h 



K^h 



|_7A (1-^) + ^ Vl=^ J" 

The concentrations of the various constituents are given by the follow- 
ing equations: 



HX = C-C.+hCr, 



K^h y,(l-h) 






K 
(56) OH- 



K^h 



K^y,{l-h) 

M-^yf^a-h) 
MOH = hC^ 

If Yg> together with the reaction constants, are known, the concen- 
trations of the constituents may be calculated. The equations may be 
generalized by introducing the ionization function K. for the salt by 

o 

means of the equation: 

(67) M^ X X- = i? MX. 

o 

This leads to the equation: 



HOMOGENEOUS IONIC EQUILIBRIA 227 

These equations are independent of the concentration of the various 
reacting constituents so long as the assumed conditions are fulfilled In 
many instances they may be greatly simplified for practical purposes. 
If the concentration of the salt is not extremely low and if the acid is 
stronger than the base, the concentration of the hydroxyl ions may be 

K h 

neglected in comparison with that of the M+ ions, and the term ~ 

may be dropped out of the equations. If the hydrolysis is small, the 
concentration of the hydrogen ions may be neglected in comparison 'with 
that of the M+ ions. The equation, then, reduces to the form: 

If acid and base are present in equivalent amounts, the hydrolysis of the 
.salt is expressed by the equation: 

(60) ^' ^^w^i' , ^w^s 



and the hydrogen ion concentration by: 

(61) H- = ^ ^-^ . 



These equations are generally applicable, provided the concentration of 
the hydrogen ions is relatively small in comparison with that of the ions 
of the salt. In the case of a solution of a strong acid and a weak base, 
the second term in Equation 60 is evidently determinative of the degree 
of hydrolysis of the salt, while in solutions in which both the acid and 
base are very weak and the total concentration of the base is high, the 
first term is chiefly determinative of the hydrolysis. In the case of acids 
and bases of intermediate strength, and particularly at fairly low con- 
centrations, both terms must be taken into account in determining the 
hydrolysis of a salt. 

In very dilute solutions of salts of relatively strong acids and bases, 
it is possible that conductance measurements may be appreciably affected 
by hydrolysis. This is particularly true if the limiting values of the 
ionization constant approached by acid and base differ. It is obvious 
that the actual concentration of acid and of base in solution is very low, 



228 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

and the values of the ionization functions to be introduced for acid and 
base are therefore not the values for these ionization functions at ordi- 
nary concentrations of acid and base, but rather the values approached 
at very low concentrations. Actually, we do not know the limiting value 
which the ionization functions approach in aqueous solutions of strong 
acids and bases. Consequently, conductance measurements with dilute 
salt solutions remain in doubt so long as the values of the ionization 
functions remain unknown. It is fairly certain that in the case of salts 
of weaker bases, such as the silver salts, for example, the conductance 
must be measurably affected at concentrations below 10"^ normal. Ac- 
cording to Bottger,^ the ionization constant of silver oxide at 25° is 
2.5 X 10~*. Assuming for the ionization constant of water the value 
0.91 X 10"" and assuming that the ionization of the salt is practically 
complete, we obtain the following values for the hydrolysis of silver 
salts at 25°. 

TABLE LXXXV. 
Hydeolysis of Silver Salts at Different Concentrations at 25°. 

C 10-^ 10* 10" 

h 1.9X10* 6.0X10* 1.9 XIO-* 

Cond. inc 5.7 X 10* 1.8 X 10"^ 5.7 X 10"^ 

As a result of the replacement of Ag+ ions by H+ ions in the solution, 
the conductance is increased approximately in the ratio of one to three. 
In the third line of the above table are given values of the increase in 
the conductance due to the hydrolysis, of the salt. It is seen that even 
at 10"^ normal the conductance of a silver salt is affected to the extent 
of 0.057%, while in a 10"* normal solution the conductance correction 
amounts to 0.18%. That the hydrolysis of salts of the weaker bases 
becomes appreciable at higher temperatures is indicated by the work 
of Noyes and Melcher * with the salts of silver and of barium. In the 
case of silver nitrate, at higher temperatures, a deposit of silver was 
formed over the inner walls of the platinum-lined bomb. This pre- 
sumably was the result of a precipitation of silver oxide, which is unstable 
at these temperatures and decomposes to metallic silver and oxygen. 

The extent of the hydrolysis of salts of strong acids and bases is very 
uncertain. At the higher concentrations, these electrolytes appear to be 
ionized somewhat more strongly than typical salts. Washburn has de- 
duced the value of 0.02 as the limit approached by the ionization con- 
stant of potassium chloride at low concentrations. But this value really 

"Bottger, ZtacJvr. /. phys. Chem. ],€, 602 (1903). 
« Noyes, Carnegie Publication, No. 63, p. 94, 



HOMOGENEOUS IONIC EQUILIBRIA 229 

represents an upper limit and it is possible that the true value may be 
much below this limit. The high value of the ionization, however, ren- 
ders any precise determination of the limiting value of the mass-action 
function uncertain, and, indeed, if conductance data alone are considered 
it is even uncertain that a definite limit greater than zero is approached.*" 
The strong acids and strong bases are ionized to practically the same 
extent at higher concentration ; and if the ionization functions in the case 
of these two types of electrolytes approach the same limits at low con- 
centrations, the conductance of a salt as measured will be found some- 
what lower than the true value if hydrolysis becomes appreciable. On 
the other hand, if the functions of acid and of base approach values which 
differ considerably, then the result will be to increase the conductance of 
the solution above that of the unhydrolyzed salt. If, for example, the 
ionization constant of the acid relative to that of the base were lO'', 
then, at a salt concentration of 10"^ N, the hydrolysis would have a value 
of 0.95 X 10"^ or approximately 0.1 per cent, which would raise the con- 
ductance of the solution approximately 0.3 per cent. In view of the 
entire lack of experimental data relating to the limiting values of the 
ionization constants of the strong acids and bases, conductance measure- 
ments with salts at concentrations below 10"* normal cannot be inter- 
preted with certainty. 

In solutions of salts of weaker acids and bases, hydrolytic equilibria 
appear to be fairly well established. This lends support to the view that 
the ionization constants of the weaker acids and bases, as well as that 
of water, are not materially affected by the presence of larger amounts 
of salt. The agreement of the values for the ionization constant of 
water as determined from a measurement of the conductance of solutions 
of salts of weak acids and bases, with that as determined by other 
methods, indicates that the fundamental assumptions underlying the 
theory of hydrolytic equilibria are substantially correct. In these equi- 
libria, the ionization of the salt is involved. If, as some assume, the 
salts are completely ionized at all concentrations, then the ionization y 

of the salt should vanish from the hydrolysis equation, which would 
materially affect the values obtained for the ionization constant of water. 
At the present time, however, data making such a comparison possible 
are not sufficiently precise to enable us to draw any certain conclusions. 

Among other typical equilibria involving electrolytes are those in 
which a strong acid or a strong base is partitioned between two weaker 

'" Naturally, if this view were adopted, it would be necessary to recast our notloDS 
relative to the nature of electrolytic equilibria. 



230 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

bases or weaker acids.^ A considerable number of equilibria of this type 
have been investigated and, in general, the results confirm the assump- 
tion that the strong base or acid is distributed between the weaker acids 
or bases in conformity with the law of mass-action. 

Equilibria similar to hydrolytic equilibria in aqueous solutions have 
been found to exist in solutions in non-aqueous solvents. Such equi- 
libria are to be expected in the case of all distinctly acid solvents which 
are capable of yielding a hydrogen ion. This, therefore, includes solu- 
tions in all acids, such as hydrocyanic acid, formic acid, acetic acid, etc. 
It likewise includes solutions in hydrogen derivatives whose acid prop- 
erties are extremely weak, such as ammonia, for example. 

Franklin " has shown that equilibria of the hydrolytic type exist in 
solutions in liquid ammonia. In the case of salts of very weak bases, 
such as mercury for example, ammono-basic salts are precipitated when 
the neutral salt is dissolved. These precipitates are redissolved on the 
addition of an acid, while precipitation is facilitated by the addition of 
an ammono-base, such as potassium amide. While equilibria of the 
hydrolytic type thus exist in ammonia solutions, the evidence indicates 
that it is only in the case of extremely weak bases that hydrolysis takes 
place to an appreciable extent. The concentration of hydrogen ions in 
ammonia is without doubt of an exceedingly low order. This is indicated 
by the fact that salts whose ammono-bases are practically insoluble in 
liquid ammonia, such as calcium and barium nitrates, for example, yield 
clear solutions when dissolved in ammonia, even at high concentrations. 
Furthermore, as is well known, solutions of the alkali metals, as well as 
of metals of the alkaline earths, in liquid ammonia, are comparatively 
stable. It is to be expected that such would not be the case if the con- 
centration of the hydrogen ions were appreciable. 

Schlesinger^ has shown that solutions of salts in formic acid are 
appreciably hydrolyzed. He found that on passing a current of air 
through solutions of chlorides in formic acid free hydrochloric acid is 
carried over. That hydrolysis may occur in solutions in other solvents, 
such as hydrocyanic acid, for example, is indicated by the high value of 
the residual specific conductance of the pure solvents. It is, of course, 
possible that in these cases the conductance is in a measurable degree 
due to the presence of impurities, but the high value obtained in many 
instances is probably due to the presence of hydrogen ions. It is prob- 
able, moreover, that the higher the dielectric constant of the medium, the 
greater the concentration of hydrogen ions due to the solvent. No 

•Thlel and Eoemer, Ztsclir. f. pJws. Ohem. 61, 114 (1908) 
•Franklin, J. Am. Ohem. 8oc. 27, 820 (1905). 
'ScWestoger, J. Am. Ohem. Soo. S3, 1932 (1911). 



HOMOGENEOUS IONIC EQUILIBRIA 231 

systematic study has been made of reactions of tlie hydrolytic type in 
non-aqueous solvents. 

Certain solvents, such as sulphur dioxide, acetone and bromine, for 
example, appear to be of a non-polar type. In these cases it is to be 
expected that equilibria of the hydrolytic type do not exist. In the case 
of polar solvents, however, we may expect equilibria of the hydrolytic 
type even though hydrogen ions are not involved. Mercuric chloride 
may serve as an example of this type of solvents. This salt, when fused, 
dissolves typical binary salts and yields solutions which conduct the 
current with considerable facility. If a salt of the type of potassium 
nitrate, for example, were dissolved in mercuric chloride, reaction might 
be expected to take place, with the formation of potassium chloride and 
mercuric nitrate in the solution. This reaction is obviously of the hydro- 
lytic type. Indeed, we see that reactions of the type MX + NY = 
KX -f MY, which take place in mixtures of fused salts, are of the 
hydrolytic type. We have here, however, an extreme case in that, in all 
likelihood, the ionization of the solvent itself is extremely high, whereas 
in the case of ordinary hydrolytic reactions the ionization of the solvent 
is exceedingly low. There is reason for believing that examples exist of 
' equilibria of the hydrolytic type intermediate between those of water 
and those of mixtures of fused salts. 



Chapter X, 

Heterogeneous Equilibria in Whicli Electrolytes 
Are Involved. 

1. The Apparent Molecular Weight of Electrolytes in Aqueous Solu- 
tion. If an electrolyte is dissolved in a solvent in equilibrium with a 
second phase, the thermodynamic potential of the solvent is displaced, 
and a displacement in equilibrium results. On the addition of an elec- 
trolyte to water, therefore, we should expect a change in the solubility 
of substances in this solvent; or, in case water itself appears as a second 
phase, we should expect a displacement in the freezing point, boiling 
point, etc. 

The earlier experiments on the freezing point of aqueous salt solutions 
indicated a fairly close agreement between the ionization as determined 
by conductance measurements and that as determined from freezing point 
measurements. These data have been examined and collected by Noyes 
and Falk.^ In solutions of the binary salts the agreement is, on the 
whole, fairly close in dilute solutions, although in the more concentrated 
solutions deviations, which exceed possible experimental errors, make 
their appearance. In solutions of potassium chloride the two methods 
yield practically identical results up to concentrations as high as 0.1 
normal. 

In order to calculate the molecular weight of a substance from the 
freezing point of its solution, the laws governing the equilibrium in the 
mixture must be known. Since the general case has been worked out 
only for dilute solutions, it is obvious that the ionization of electrolytes, 
and the molecular condition of substances in general, may not be deter- 
mined from freezing point determinations at higher concentrations. 
Washburn and Maclnnes ^ showed that, while the freezing point curve 
for potassium chloride corresponds very nearly with that of a solution 
of sugar in water up to fairly high concentrations, those for solutions of 
lithium chloride and caesium nitrate exhibit deviations at fairly high 
dilutions. The deviations in the case of the last named salts lie in oppo- 
site directions from the theoretical curve of ideal solutions. They found, 

'Noyes and Falk, J. Am. Ghem. 8oc. SS, 1437 (1911). 

a Washburn and Maclnnes, J. Am. Ohem. 8oc. S3, 1686 (1911). 

232 



HETEROGENEOUS EQUILIBRIA 233 

however, that at lower concentrations the curves for the three salts ap- 
proach that of an ideal system, assuming the ionization to be given by 

the conductance ratio -i-. 
Ao 

More recently the methods for determining the temperature of solu- 
tions in equilibrium with ice have been greatly refined, and molecular 
weight determinations are available at very low concentrations. In 
Table LXXXVI, under 7^ are given values of the ionizatioq for potassium 

chloride at low concentrations as determined by Adams '" and by Bed- 
ford.* Under y^ are given values of the ionization at the same concen- 
trations as determined from conductance measurements. 

TABLE LXXXVI. 

Comparison of the Ionization Values for Potassium Chloride from 
Freezing Point and Conductance Measurements. 



xio^ 


y- (Adams) 


Yj- (Bedford) 


Vc 


2 


0.969 


.... 


0.971 


5 


0.961 


0.959 


0.956 


10 


0.943 


0.939 


0.941 


20 


0.922 


0.915 


0.922 


50 


0.888 




0.889 


100 


0.861 


• ■ • • 


0.860 



An examination of this table shows that the ionization values as deter- 
mined by the freezing point method correspond within the limits of error 
with those as determined by the conductance method. The temperature of 
the conductance measurements, in this case, was 18°, while that of the 
freezing point measurements was necessarily in the neighborhood of 0°. 
It is known, however, that at fairly high dilutions the ionization of salts 
varies only little between 0° and 18°. The results are therefore com- 
parable. 

In Table LXXXVII are given values of the ionization as determined 
from freezing point and conductance measurements for solutions of potas- 
sium nitrate, potassium iodate, sodium iodate, and for equi-molar mix- 
tures of potassium chloride and potassium nitrate, and potassium iodate 
and sodium iodate." 

Examining the results given in the following table, it is evident that, 
in the case of potassium nitrate, the ionization values by the two methods 

•Adams, J. Am. Chem. Soc. SI, 482 (1915). 

•Bedford, Proc. Roy. Soc. (A) SS, 454 (1910). 

■ Hall and Harklns, J. Am. Chem. Soc. SB, 2658 (1916). 



234 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE LXXXVII. 

Comparison of the Ionization Values of Salts as Derived from 
Freezing Point and Conductance Measurements. 

Potassium Nitrate 



CXIO' 


Y^ (Adams) 


Vc 


2 


0.967 


0.970 


• 5 


0.958 


0.953 


10 


0.937 


0.935 


20 


0.908 


0.911 


50 


0.848 


0.867 


100 


0.787 
Potassium lodate 


0.824 


cxio= 


Y^ (Hall & Harkins) 


Yc 


2 


0.940 


0.965 


5 


0.929 


0.946 


10 


0.916 


0.928 


20 


0.890 


0.903 


50 


0.835 


0.860 


100 


0.764 

Sodium lodate 


0.819 


CXIO' 


Y^ (Hall & Harkins) 


Yc 


2 


0.950 


0.960 


5 


0.934 


0.939 


10 


0.915 


0.917 


20 


0.890 


0.890 


50 


0.832 


0.842 


100 


0.772 


0.801 



Equal Molecular Mixtures of KCl and KNO^ 

CXIO' Y^ (Hall & Harkins) 

10 1.94 

20 1.914 

50 1.868 

100 1.827 

200 1.773 

Equal Molar Mixtures of KIO^ and NalO^ 

C X 10' y. (Hall & Harkins) 

10 1.912 

20 1.890 

50 1.834 

100 1.768 



HETEROGENEOUS EQUILIBRIA 235 

agree at concentrations below 20X10"^ N. At higher concentrations, how- 
ever, the freezing point method yields lower values than the conductance 
method. In the case of potassium iodate, the agreement is not so good. 
At the lower concentrations the value of the ionization as determined by 
the conductance methods is about 1.5 per cent higher than that deter- 
mined by the freezing point method. The limiting value of the conduct- 
ance of the iodates is much less certain than is that of the chlorides and 
nitrates, and it is possible that the ionization values, as determined by 
this method are in error owing to an error in the value of Ao. If the 
value of Ao were increased by 1.5 per cent, the conductance values for 
potassium iodate would agree up to a concentration of 0.05 normal. In 
solutions of sodium iodate, the discrepancies exceed the limit of experi- 
mental error, of the* conductance measurements, at any rate. It is pos- 
sible that here, also, an error in the value of Ao would tend to harmonize 
the results. 

As regards the freezing point of equi-molar mixtures of two electro- 
lytes, it is interesting to note that the values of i for the mixtures are 
practically the mean of those for the pure substances at the same concen- 
tration. 

In Table LXXXVIII are given values of i for salts of higher type,« 
together with values of y^ and y^, where reliable values of y^ are 

available. 

TABLE LXXXVIII. 

Ionization op Salts of Higher Type as Determined by the Freezing 
Point and Conductance Methods. 

C X 10' i (Hall & Harkins) y^ (Hall & Harkins) y^ 

Magnesium Sulphate, MgSO^ 

5 1.708 0.708 0.741 

10 1.614 0.614 0.669 

20 1.520 0.520 0.596 

50 1.394 0.394 0.506 

100 1-303 0.303 0.449 

200 1.214 0.214 0.403 

500 1.099 0.099 

Potassium Sulphate, X2SO4 

5 2.830 0.915 0.905 

10 2.772 0.886 0.872 

20 2.701 0.851 0.832 

50 2.567 0.784 0.771 

100 2.451 0.726 0.722 

200 2.327 0.664 0.673 

• Hall and Harkins, loc. cit. 



236 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 
Barium Chloride, BaCl^ 



5 


2.847 


0.924 




10 


2.790 


0.895 


0.883 


20 


2.730 


0.865 


0.850 


50 


2.647 


0.824 


0.798 


100 


2.585 


0.793 


0.759 


200 


2.535 


0.768 


0.720 




Cohalt Chloride, CoCl^ 




5 


2.858 


0.929 




10 


2.802 


0.901 




20 


2.749 


0.875 




50 


2.687 


0.844 






Lanthanum Nitrate, La{N0s)3' 




5 


3.694 


0.898 




10 


3.578 


0.859 


6.802 


20 


3.440 


0.813 




50 


3.261 


0.754 


6.701 


100 


3.149 


0.716 




200 


3.063 


0.688 





500 


3.002 


0.667 






The agreement between the ionization values as determined from 
conductance and freezing point measurements, in the case of the salts of 
higher type, is not as close as in that of the binary salts. The devia- 
tions in the more dilute solutions are in the neighborhood of one per cent, 
for the uni-divalent salts. In solutions of potassium sulphate the ioniza- 
tion values by the freezing point method are slightly higher than those 
by the conductance method, except at a concentration of 0.2 normal, 
where the conductance method gives a slightly higher value. On the 
whole, for this salt the agreement is fairly close and it is possible that 
the discrepancies which remain may be due to error in the value of Ao 
employed. In the case of barium chloride, the ionization values by the 
freezing point method at the lower concentrations are slightly over one 
per cent higher than those by the conductance method. At the higher 
concentration the difference in the values increases to five per cent at 
0.2 normal. The differences at the lower concentrations may arise from 
uncertainties in the values of A„, but at the higher concentrations there 
is evidently a definite divergence between the two curves. Accurate con- 
ductance values for cobalt chloride are not available. The values of i 
however, do not differ greatly from those of barium chloride or potassium 
sulphate. 

In solutions of lanthanum nitrate, the ionization values as deter- 



HETEROGENEOUS EQUILIBRIA 237 

mined by the freezing point method are approximately seven per cent 
greater than those determined by the conductance method. Comparison, 
however, can be made only at two concentrations. The discrepancies 
in the values appear to be greater than might be expected from any 
possible errors in the assumed value of Aq. In the case of magnesium 
sulphate, there is a marked divergence between the values of the ioniza- 
tion as determined by the two methods. However, as the concentration 
decreases, the ionization curves, as given by the two methods, approach 
each other. 

Considering these results broadly, it may be concluded that the freez- 
ing point and the conductance methods give values for the ionization 
which fall very nearly within the limits of experimental error at concen- 
trations approaching 10"° normal for solutions of the binary salts, and 
that in the case of solutions of salts of higher type the differences between 
the values, as determined by the two methods, do not, in general, exceed 
one per cent at low concentrations for salts of the uni-divalent type. 
For salts of the di-divalent type, the discrepancies between the values, . 
as determined by the two methods, are markedly greater, lying in the 
neighborhood of 5 per cent, and the same is true of lanthanum nitrate. 
In general, however, in the case of salts of higher type, the divergence 
of the values determined by the two methods diminishes as the concen- 
tration decreases. 

Considering the results of freezing point determinations, it is a strik- 
ing fact, the significance of which cannot be ignored, that, as the concen- 
tration decreases, the molecular depression of the freezing point increases 
and approaches a limiting value, which, in the case of salts of different 
types, corresponds with the ionic structure of these salts and which is 
in agreement with the fimdamental ionic reactions assumed by the ionic 
theory. So the value of i for the binary salts approaches a value of 2, for 
ternary salts 3, for quaternary salts 4, etc. While the significance of the 
agreement between the results of freezing point and conductance meas- 
urements remains uncertain, the fundamental importance of the fact that 
the limits approached in the two cases are substantially the same should 
not be overlooked. 

The difference between the results by the two methods at the higher 
concentrations are readily explainable, since the calculation of the num- 
ber of molecules present in a mixture is based upon the assumption that 
the laws of dilute solutions hold. Even in the case of non-electrolytes, 
the laws of dilute solutions fail to hold at concentrations as low as 0.1 
normal, and it is therefore a priori probable that the laws of dilute solu- 



238 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tions in electrolytic systems will fail at concentrations below this value. 
Furthermore, in the case of salts of higher type, it is not improbable that 
intermediate ions are formed, as a result of which a divergence will arise 
between the results as determined by conductance and by osmotic 
methods. 

Nernst ' has called attention to the fact that, since the law of mass- 
action in its simple form does not hold for solutions of strong electrolytes, 
the laws of dilute solutions cannot be applied to these mixtures. As a 
consequence, if the ionization is correctly determined by the conductance 
method, the ionization as determined by osmotic methods, assuming the 
laws of dilute solutions to hold, should differ from that determined by 
conductance measurements. It appears, however, that in the case of 
certain electrolytes, such as potassium chloride, osmotic methods and 
conductance methods lead to the same value of the ionization, and, in 
the case of other electrolytes, the two methods lead to very nearly the 
same value at concentrations approaching 10"^ normal. Yet, in the 
neighborhood of 10"^ normal, strong electrolytes do not conform to the 
simple law of mass-action. Those who would use the results of osmotic 
methods to substantiate the correctness of the results of conductance 
methods thus find themselves in a dilemma, for, if the two methods lead 
to identical values of the ionization, then, if the results of osmotic meas- 
urements are looked upon as correct, the interpretation of conductance 
measurements must be in error, while, if the results of conductance meas- 
urements are accepted in their usual sense, the laws of dilute solutions 
are inapplicable. That the concordance of the ionization values deter- 
mined by conductance and osmotic methods at low concentrations is an 
accidental one is very improbable. It appears, rather, that this agree- 
ment is the expression of a fundamental property of such solutions. The 
significance of this agreement, however, remains uncertain. This ques- 
tion will be discussed further in the next chapter. 

The molecular weight of electrolytes in aqueous solutions has like- 
wise been determined from the measurement of the elevation of the boil- 
ing point. The precision of such measurements is necessarily much 
lower than that of the freezing point depression and need not be discussed 
in detail here. The molecular weight of electrolytes in aqueous solutions 
has also been determined from vapor pressure measurements.' The 
experimental difficulties attending the use of this method are very great 
and it is doubtful if the precision of such determinations equals that of 

'Nernst, Ztschr. f. phjja. Chem. 38, 494 (1901). 

•Lovplaci', Jn-azcr ancj Sease, /. Am, Chen. Boc. IfS, 102 (18?1), 



HETEROGENEOUS EQUILIBRIA 239 

the freezing point method. The results obtained agree well with those 
obtained by the freezing point method.*^ 

2. The Molecular Weight of Electrolytes in Non-Aqueous Solutions. 
A great many measurements have been made of the molecular weight of 
electrolytes in various non-aqueous solvents. With a few exceptions, 
the boiling point method has been employed. The resulting data suffer, 
consequently, from the inaccuracies inherent in this method. Measure- 
ments at low concentrations appear to be entirely lacking. In general, 
in solvents of fairly high dielectric constant, where the ionization is com- 
parable with that in water, the molecular weights as determined lie 
below the normal values and indicate ionization. In solvents of fairly 
low dielectric constant, usually below 20, the apparent molecular weight 
rarely indicates ionization at higher concentrations. 

The most extensive molecular weight determinations in a non- aqueous 
solvent have been made by Walden and Centnerszwer " with solutions in 
sulphur dioxide. In Table LXXXIX are given values of the van't Hoff 
factor i for various electrolytes dissolved in sulphur dioxide at dilutions 
from 1 to 16 liters. An inspection of the table shows that, at a dilution 

TABLE LXXXIX. 
Values of i for Electrolytes Dissolved in Sulphur Dioxide. 

v= 1 2 4 8 16 

1. KJ 0.42 0.55 0.63 0.74 0.86 

2. KCNS 0.41 0.49 0.60 0.68 0.71 

3. NaJ 0.57 

4. NHJ 0.41 0.53 0.64 0.71 0.82 

5. NH.CNS 0.29 0.40 

6. RbJ 0.52 0.61 0.73 0.82 0.85 

7. N(CH3)H3C1 0.28 0.38 0.49 0.62 0.81 

8. N(CH3)2H,C1 0.87 0.79 0.76 0.82 0.86 

9. N(CH3)3HC1 1.12 1.00 0.99 0.96 0.96 

10. N(CH3),C1 1.16 1.08 1.05 1.03 1.02 

11. N(CH3),Br 1.30 1.10 1.01 0.97 0.95 

12. N(CH,),J 1.26 1.20 1.16 1.18 1.23 

13. N(CA)H3C1 0.43 0.50 0.62 0.68 0.71 

14. NCC.HJ.H^Cl 0.70 0.69 0.70 0.76 0.78 

15. N(C,HJ3HC1 1.15 1.06 1.06 1.05 1.06 

16. N(C2HJ,J 1.61 1.39 1.27 1.17 1.11 

17. N(aH,)H3Cl 0.44 0.51 0.59 0.72 0.80 

18. S(CH3)3J 0.84 0.97 1.03 1.06 1.08 

••According to Heuse (Thesis, Univ. of 111., 1914), the agreement between the con- 
ductance and the vapor pressure method does not hold for KCl at 25°. See also Wash- 
burn, "Principles of Physical Chemistry," Ed. 2, p. 268. 

•Walden and Centnerszwer, Ztschr. J. pltys. Chem. 39, 518 (190?), 



240 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

of 16 liters, a few salts have a value of i greater than unity, while the 
greater proportion of the salts has a value of i less than unity. At 
higher concentrations the curves exhibit a very complex form. In the 
case of most of the substances which have a relatively high value of i at 
lower concentrations, the value changes but little until a concentration 
of 0.2 normal is reached, when the value of i begins to increase rapidly 
with increasing concentration. In the case of salts having a low value of 
i at the lower concentrations, the value of i, in general, decreases with 
increasing concentration, particularly as normal concentration is ap- 
proached. Certain of the electrolytes exhibit an exceptional behavior 
in that the curves of the i values intersect those of the majority of the 
electrolytes. It is evident that molecular weight determinations in sul- 
phur dioxide are uncertain in their significance. On the whole, the curves 
exhibit a definite trend as the concentration decreases indicating that the 
value of i will ultimately rise above unity. It is to be borne in mind 
that the ionization of salts in sulphur dioxide is relatively low, being in 
general less than 20 per cent in the neighborhood of 0.1 normal. Further- 
more, even in the case of aqueous solutions, freezing point and con- 
ductance methods lead to divergent results at higher concentrations. If 
the divergence of a solution of an electrolyte from the simple laws of 
dilute solutions is in any considerable measure due to the electrostatic 
action of the charged particles upon one another or upon the solvent me- 
dium, then it is to be expected that as the dielectric constant of the sol- 
vent is smaller, the divergence at a given concentration will be greater, 
since the force due to a charged particle varies inversely as the dielectric 
constant. It seems not improbable, also, that, in the case of certain sol- 
vents, polymerization may take place to a considerable extent at higher 
concentrations. This would greatly complicate the behavior of these solu- 
tions and would make it impossible to interpret either the results of 
conductance or of osmotic measurements. 

The molecular weights of a number of electrolytes in liquid ammonia 
at its boiling point have been determined by Franklin and Kraus ^° from 
the boiling point measurements. Owing to the exceptionally low value 
of the boiling point constant of liquid ammonia, about 3.4, measurements 
below 0.1 normal were not made. ■ As a consequence, the determinations 
relate almost entirely to concentrations at which it might be expected that 
the laws of dilute. solutions would not hold. In general, in the neighbor- 
hood of 0.1 normal, the observed elevation of the boiling point corre- 
sponds approximately with a normal value of the molecular weight of 
the dissolved electrolyte. At higher concentrations, the molecular eleva- 

■» Franklin and Kraus, Am. Chem. J. W, 838 (1898). 



HETEROGENEOUS EQUILIBRIA 241 

tion of the boiling point increases in the case of all the salts measured. 
It is obvious that in these solvents the concentration at which the meas- 
urements were carried out is too high to admit of a comparison with 
the results of the conductance method. In comparing the results of the 
conductance method with that of other methods of determining the degree 
of ionization of salts in non-aqueous solvents, it should be borne in mind 
that, according to conductance measurements, the deviations from the 
law of simple mass-action increase greatly as the dielectric constant of 
the medium decreases. If, then, the deviations from the laws of dilute 
solutions lead to a lack of correspondence between the results of the , 
osmotic and the conductance methods, the discrepancy between the results 
of the two methods should be the greater, the greater these deviations. 
It might be expected, therefore, that, in solvents of low dielectric con- 
stant, the discrepancies would prove to be very great. 

In solvents of fairly high dielectric constant, molecular weight deter- 
minations by osmotic methods yield values for the ionization which are 
comparable with those resulting from conductance measurements, and 
the ionization increases as the concentration decreases. In making such 
comparisons, however, it should be borne in mind, not only that the ex- 
perimental errors are great in the osmotic determinations, but, also, that 
the conductance values are more or less uncertain, and that the values 
of Ao are often subject to considerable errors. In the following table are 
given values of the ionization y- as determined from conductance meas- 
urements and Y), as determined from the elevation of the boiling point 
for solutions of (CjIIs)^^ in a number of solvents." 

TABLE XC. 

Values of i for Solxttions in Different Solvents. 

CH3OH CH3CN 

V 3 6 12 V 10 15 



J 0.38 0.45 0.52 y^ 0.48 0.54 

0.24 0.29 0.38 Y5 0.49 0.57 

CH.OH C,H,CN 



-^2-" 



7 30 F 30 

Y, 0-41 Yc 0-53 






0.30 Yfe 0-54 

"Walden, Ztsohr. f. phys. Chem. 5S, 281 (1906). 



242 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

While the correspondence between the two methods is not very exact, 
nevertheless it is evident that the relations in these solvents are similar 
to those found in aqueous solutions. 

In pyridine the values of i are in general less than unity, as may be 
seen from the following table. 

TABLE XCI. 
Values of i for Solutions in Pyridine. 
AgNOs (C,H3),NI 

V= 1 2 8 V= 16 32 

1= 0.77 0.75 0.91 i= 0.73 0.82 

The molecular weight of sodium iodide in acetone has been deter- 
mined by McBain and Coleman.^^ -phe values obtained are very nearly 
normal from 0.9 to 0.04 normal concentrations. If anything, the mole- 
cular weights are slightly larger at the lower concentrations. At these 
concentrations, the conductance method indicates an ionization varying 
from 17 to 43 per cent. It is evident that in this solvent the results of 
conductance and of osmotic measurements are not in agreement. In 
acetone, however, the deviations from the law of simple mass-action are 
large, and there is evidence that polymerization of the dissolved salts 
takes place, presumably with the formation of complex ions.^^* This 
renders the interpretation of results in, the more concentrated solutions 
diflBcult. 

Phenol is the only non-aqueous solvent in which the molecular weights 
of salts have been determined at relatively low concentration. Riesen- 
feld,^' from the freezing point of a saturated solution of potassium iodide 
in phenol, whose concentration is 0.0045 normal, obtained a value of 170, 
for the molecular weight of potassium iodide, which corresponds closely 
with the normal value of 166. The equivalent conductance of solutions 
of potassium iodide in phenol al these concentrations is of the order of 
1.0. Hartung^^ has measured the molecular weights of a number of 
salts in phenol by the freezing point method. These include tetramethyl- 
ammonium iodide, sodium acetate, aniline hydrochloride, dimethylamine 
hydrochloride, as well as several organic salts of alkali metals. The 
concentrations run to dilutions, in some cases, as low as 0.01 normal. In 
the following table are given the values obtained for i for solutions of 
tetramethylammonium iodide and sodium acetate in phenol. With 
aniline hydrochloride, i has a value of unity at a concentration of 0.02 N 

"McBaln and Coleman, Trans. Faraday Soc. 15. 45 (1919) 
"« Serkov, Ztschr. f. phys. Chem. 73, 567 (1910). 
" Rlesenfeld, Ztschr. f. phys. Chem. 1,1, 346 (1902). 
"Hartung, Ztschr. ). phys. Otiem. 77. 82 (1911). 



HETEROGENEOUS EQUILIBRIA 243 

and decreases to values less than unity at higher concentrations. In the 
case of dimethylamine hydrochloride i has a value of 1.18 at F = 23, 
and decreases to a value in the neighborhood of unity at a dilution of 

TABLE XCII. 

MoLECULAK Weights of Salts in Phenol. 



Tetrame 


ithylammonium Iodide. 


Af = 201.1 


V 


M(obs.) 


i 


92.7 


135.5 


1.48 


38.9 


143.5 


1.40 


22.9 


150.2 


1.34 


12.3 


163.9 


1.23 


8.18 


171.5 


1.17 


5.70 


177.6 


1.13 


4.75 


182.6 


1.10 


4.08 


185.4 


1.08 


3.52 


188.8 


1.07 


3.05 


189.0 


1.06 


2.67 


190.0 


1.05 


2.40 


191.1 


1.05 


2.10 


191.5 


1.06 


1.73 


188.9 


1.07 


1.59 


185.3 


1.08 




Sodium Acetate. M = 


:82.1 


V 


M{ohs.) 


i 


41.8 


46.6 


1.75 


29.5 


48.8 


1.66 


20.5 


54.0 


1.51 


16.3 


57.5 


1.43 


13.3 


59.9 


1.37 


11.4 


61.8 


1.33 


9.68 


63.5 


1.30 


8.70 


65.0 


1.27 


7.62 


66.5 


1.23 


6.86 


67.1 


1.22 


5.89 


68.0 


1.20 


5.12 


69.5 


1.19 


4.43 


70.2 


1.16 


3.85 


72.0 


1.14 


3.37 


73.5 


1.11 


2.98 


76.7 


1.06 


2.65 


78.4 


1.04 


2.37 


81.0 


1.01 


2.15 


82.9 


0.99 


2.0 


83.0 


0.99 



244 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

2 liters. As may be seen from the table, the value of i for tetramethyl- 
ammonium iodide in the neighborhood of 0.01 N is approximately 1.50, 
while that for sodium acetate is even higher than that of tetramethyl- 
ammonium iodide, being 1.75 at 7 = 41.8. 

Phenol has a dielectric constant of 9.68 and the high values obtained 
for i are unexpected. The conductance of solutions of tetramethylam- 
monium iodide in phenol at 45° has been measured by Kurtz.^** The 
constants for these solutions are m = 1.28, D = 0.69, X = 2.3 X 10'* 
and Ao = 16.67. Solutions of tetramethylammonium iodide in phenol 
thus exhibit an ionization not very different from that found for solutions 
of typical salts in other solvents, having a dielectric constant in the 
neighborhood of 10. While the ionization is marked at the lower con- 
centrations, the value is much lower than corresponds to the value of i 
found by Hartung. Thus, at a concentration 0.01 N, the ionization from 
the conductance values is 0.194 in contrast to 0.48 from freezing point 
determinations. 

It is evident that there is a wide discrepancy between the values of 
the ionization as determined by the two methods. It is particularly 
striking that the values of i found for salts of weak organic acids are 
higher than those for typical electrolytes. Since phenol is an acid sol- 
vent, it is probable that a solvolytic reaction takes place when a salt is 
dissolved in phenol according to the equation: 

PhOH + MX = MOPh + HX. 

If this were the case, we should expect the greatest values of i in the 
case of salts of weak acids and bases, which would account for the high 
values found for solutions of tetramethylammonium iodide and sodium 
acetate. Lacking further experimental material, however, the question 
must be left open. 

The results obtained from molecular weight determinations indicate 
that, in solvents of intermediate dielectric constant, the values of y 
approach those of y^ at low concentrations. At high concentrations the 
divergence is often great and the variation of the i values depends greatly 
on the nature of the electrolyte. In solvents of dielectric constant lower 
than 20, the values of y by the two methods are not in agreement. This 
is not surprising, since these solutions may be expected to show large 
divergences from the laws of ideal systems. So far as may be judged 
from the available material, however, at very low concentrations, y and 
7g approach a common limit in non-aqueous solutions. The corre- 

"• Kurtz, Thesis, Clark Univ. (1920). 



I 



HETEROGENEOUS EQUILIBRIA 245 

spondence found between the values of y- and y in aqueous solutions 

appears, therefore, to be a property of electrolytic solutions in other 
solvents also. 

3. Solubility of Non-Electrolytes in the Presence of Electrolytes. 
The solubility of non-electrolytes in water is, in the majority of cases, 
depressed by the addition of an electrolyte. The effect of the added 
electrolyte on the solubility depends upon the nature of the substance in 
question, as well as upon that of the added electrolyte. If reaction takes 
place between the two, the solubility is naturally influenced by this 
reaction. 

For certain substances, the solubility is very nearly a linear function 
of the concentration of the added salt, in which case it may be expressed 
by the equation: 

(62) S = So + BSoC 

where So is the solubility of the non-electrolyte in pure water, S is the 
solubility in the presence of the salt at the concentration C, and B is the 
solubility coefficient, which is a constant if the solubility varies as a 
linear function of the concentration. In general, however, the solubility 
function is not a linear one. The change in the solubility for a given 
addition of electrolyte is, as a rule, the greater the smaller the amount of 
electrolyte added. The solubility is more accurately expressed by the 

equation: 

c 

(63) log -s- = PC," where p is a constant. 

Oo 

In the following table are given values for the solubility of hydrogen 
in aqueous solutions of different electrolytes.^^ In pure water, the solu- 

TABLE XCIII. 

SOLTIBILITY OF HYDROGEN IN AqXTEOUS SOLUTIONS OF ELECTROLYTES AT 

Different Concentrations at 25°. 
C= 0.5 1 2 3 4 

CHCOOH ... 0.0192 0.0191 0.0188 0.0186 0.0186 

Ch!c1C00H 0.0189 0.0186 0.0180 

HNO ... 0.0188 0.0183 0.0174 0.0167 0.0160 

HCl '..'.'.'.'.'.'.'.".' 0.0186 0.0179 0.0168 0.0159 

H2SO4 0185 0.0177 0.0163 0.0150 0.0141 

2 

KOH 0.0167 0.0142 

NaOn"'.' 0.0165 0.0139 0.0097 0.0072 0.0055 

"Rothmund, Ztschr. f. Electroch. 7, 675 (1901); ZtsoJir. f. phys. Ghem. 69. 524 
/'iQnQ'i • Nprnat ibid., 38, 494 (1901). ^ ,^ 

^^°r.'(iJcken,Zt80hr. f.phys.Chem. 1,9, 257 (1904). 



246 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



bility of hydrogen at 25° is 0.01926. The results are shown graphically 
in Figure 48. An examination of the table shows that solubility depres- 
sion is a specific property of the electrolyte. The depression due to 
chloroacetic acid is slightly greater than that due to acetic acid. Nitric, 
hydrochloric and sulphuric acids cause ,a small, but markedly greater, 
depression of the solubility. On the other hand, sodium and potassium 
hydroxides cause a marked depression of the solubility. 

The solubilities may be compared by means of the solubility coeffi- 



0.0 IS 



3 0.010 



o 

03 



COOS' 



o.ooo 



—^^__^ 










\ 


^ 


CH^CtCOQB 


Hci- 


-kUXOj 


\ 


^^'OH 






«,so. 


i 




















iaOU 



iTt zn 3it 4n 

Concentration of Added Electrolyte. 



S7l 



Fig. 48. Solubility of Hydrogen in Water at 25° in the Presence of Electrolytes 

at Varying Concentrations. 

cient for the percentage equivalent solubility change, as defined by the 
equation: 



(64) 



5' = ioo^xi 



In Table XCIV are given the values of the percentage equivalent 
solubility depression of hydrogen, corresponding to Table XCIII. If 
the solubility varied as a linear function of the concentration of the salt, 
the equivalent percentage solubility depression would be a constant. As 
may be seen by reference to Figure 48, the curves are convex towards the 
axis of concentrations, which corresponds to a decrease in the solubility 
coefiicient. In Table XCV are given values of the relative percentage 
solubility depression for nitrous oxide and in Table XCVI those for 
oxygen at 25° and 15°. It will be observed, in the first place, that the 
percentage solubility effect is in certain cases a function of the tempera- 



HETEROGENEOUS EQUILIBRIA 247 

TABLE XCIV. 

Equivalent Percentage Solubility Depression for Hydrogen in 

Water at 25°. 

C= 0.5 1 2 3 4 

CH3COOH 1.0 1.0 1.0 1.0 

CH,C1C00H 3.7% 3.4 3.3 

HNO3 4.8 4.9 4.8 4.4 4.2 

HCl 7.3 7.0 6.4 5.8 

H^SO, 

2 8.0 8.1 7.7 6.7 

KOH 26.6 26.4 

NaOH 28.6 27.9 24.8 20.9 17.9 



TABLE XCV. 

Relative Percentage Solubility Depression op Nitrous Oxide 

at 25° AND 15.° , 



C = 

HNO3 
HCl .. 
H,SO, 

2 
NH.Cl 
CsCl . 
KJ ... 
KBr .. 
LiCl .. 
RbCl . 
KCl .. 
KOH . 



t = 25° 



t=15° 



0.5 1 2 3 4 

— 1—1—1.1 .. .. 

+ 5.7 + 4.4 + 3.1 . . . . 

9.4 8.7 7.2 6.3 5.5 



12.4 
16.8 
17.8 
19.5 
19.8 
20.5 
20.6 
26.9 



10.9 

17.2 
18.3 
18.7 
18.7 
20.0 
26.6 



0.5 1 2 


+ 5.9 + 5.1 + 4.0 

11.3 10.2 8.6 



12.8 
17.5 
19.5 
20.8 
20.8 
21.3 
23.6 
28.3 



7.5 6.9 



11.2 






18.6 
19.4 
19.9 
19.7 
20.6 
28.1 







TABLE XCVI. 
Relative Equivalent Percentage Solubility Depression of Oxygen at 25° and 15° 



C = 

HNO3 
HCl .. 
H,S04 

2 
NaCl 
K.SO« 

2 
KOH . 
NaOH 



0.5 

4 
7.8 

13.0 

30.0 

35.7 

36.4 

37.7 



t = 25° 



1 


2 


3 


4 


5 


4 
6.8 


4 
6.3 


•• 


■• 


•• 


10.7 


9.4 


8.4 


8.1 


7.5 


27.6 


24.3 








32.8 










33.1 
33.8 


28.6 


•• 







0.5 



t = 15° 



1 



8.3 
10.4 


7.4 
8.9 


13,8 


12.1 


30.3 


28.4 


38.0 


34.7 


39.7 
41.3 


35.5 
36.4 



2 


3 


4 


5 


6.6 

8.8 


•' 






10.7 


9.9 


8.8 


8.3 


25.1 


•• 




•• 


30".6 


•• 


•• 


•• 



248 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ture, while in other cases the solubility effect is relatively independent of 
temperature. In the presence of nitric acid, the coeflScient for oxygen 
increases from 4 to 8 per cent, as the temperature falls from 25° to 15°. 
In the presence of hydrochloric acid the coefficient increases slightly, 
while in the presence of sulphuric acid the coefficient changes but little. 
In the presence of sodium chloride, the coefficient is practically identical 
at the two temperatures. The solubility of nitrous oxide appears to vary 
less than that of oxygen as the temperature changes. 

The order of the electrolytes in terms of their solubility effect is 
practically the same for different gases. Indeed, in many cases, the 
solubility coefficients for different gases are very nearly the same for the 
same electrolyte. An inspection of the tables will show that, in general, 
the order in which the electrolytes appear is the same. In certain cases, 
however, the solubility effects show an influence due to the nature of the 
dissolved gas. For example, in a 1.0 normal solution, the solubility 
coefficient for hydrogen in the presence of nitric acid is 4.9, that of 
oxygen is 4, and that of nitrous oxide is ^ — 1 per cent. The negative sign 
indicates that the solubility is increased on addition of the electrolyte. 
The solubility effect is smallest in the case of the acids and is greatest in 
that of the bases. The solubility coefficients for the salts are, in general, 
slightly smaller than those for the bases. 

In Table ^^ XCVII are given values of the percentage equivalent solu- 
bility depression for a variety of substances in the presence of different 
electrolytes. A comparison of the results collected in this table shows 
that the order of electrolytes as regards their effect on the solubility of 
different substances is practically identical throughout. This is particu- 
larly true in the case of those substances where reaction with the electro- 
lyte is not to be expected. The smallest effect for typical salts is ob- 
served in the case of ammonium nitrate. However, any general relation 
between the nature of the electrolyte and the nature of the solubility 
effect cannot be established. The action is specific in character. 

With a few exceptions, the addition of an electrolyte to a solution 
of a non-electrolyte in water causes a depression in the solubility of the 
non-electrolyte. This effect, which has been called a "salting out" 
effect, is not, however, characteristic of electrolytes alone. For example, 
the percentage equivalent solubility depression of hydrogen in water in 
the presence of sugar at normal concentration is 32. Similarly, the 
equivalent depression of hydrogen at the same concentration at 20° is 
9.2 for chloral hydrate. The depression for sugar is greater than that for 
most salts, while that for chloral hydrate is greater than that for the 

"Euler, Ztschr. f. phya. Ohem. p, 310 (1904). 



HETEROGENEOUS EQUILIBRIA 



249 



T3 
O 



■ lO r-H 








§ 




a> 


















H 




a 

o 


. 


. ■ lO 00 • • 


. 




t> OS • • 






O 




• 


• T— 1 


T— t 


* 




IM (M • ■ 






i 




eq 


















fS 




1 


, 


• • • 


• CO to 


, 


t^ 05 . . . 


. . . t> 








s 


• 


• • ' 


• (M IM 


• 


,-H (M • • • 


. . . Ttl 










< 




















gl5 


. 


CO O tH 


• • CO 


, 


• ^ !>• CO • 


. . • 






!? 




■ 


T—i 1— t 


• • r-t 




• --I 1-1 IM • 


• • • 






M 






















to 




w°^ 


l> 


. . CO 
' ' 1 


• • O 

• T-l 




• • CO • • 


; lO • • 






Iz; 






1 


1 


1 




. . 1 . . 








<« 






















CO 

CO 




tag 


t^ 


• ■ 00 O • -^ iC 


• 00 00 (M • 


t^ .-H 00 • 


li^ 








1 




>-l • (N IM 


■ IM IM CO • 


CO Tt< CO • 






i 






. 


CD • r-l 


• Tt< O 


. 


• <M • • • 


• CO ^ ^ 


t-l 




o 


1 


• 


(M • CO 


■ CO ■'tl 


* 


. -^ . . . 


• lO iC >o 


13 


l—i 


tS 


g 


















H- 1 






<u 












lO 


U 


>; 


1 




(—1 -4-^ 




• • (M 


• • o 




■ ■* . 05 • 


• CO • • 




o 


11 




• • 7-1 


• • CO 


■ 


• CO ■ CO • 


. ^ . . 


pq 




iz; 


^ 


1— 1 


(N lo 03 




. 


CO 

■ lo 00 ; 


IM t^ I ; 


1=1 




w 






T-H tH 




• I-H T-l 


(M (M 


<1 


E 


P3 
















^ 


H 


1^ 


[£4 
















, 1 




O 

o 




o 


CO 


; ■ a> a> t~ • 


, 


• ,-1 • o c 


• (M • • 


+J o 




Q 


o 






T-4 i-H . 


• 


• (M • CO CC 


• CO • • 






[H 


















g 




a 























►q 




c. 


, 


. . . 


. 


IM 


. ^ • • 




S 




3 




^ 




■ 


• 


CO 


. CO • • 




^ 

m 




J 






















o 

32 




o 






■^ CO 




iq 03 CO 


00 


d 
o 
■a 
5- 




"^ 






. 


■ .-H (N 




CO CO ; oj 


: 2 : : 




S 




•£ 




.■ 


(M IM 




IM (M <M 


(M 


o 



« 

H 
Ph 



P 



M 



to o 

I-H IM 



CO CO 
(M IM 



oa 



O' 



OO 



O 
02 



(M IM 



^©"o 



m'S O O oq o 

MH CO rrj 02 " .J" 



^ M M w ^ '^3 W >^^ >:-»;:? ;:r^ 



o 



250 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

acids. Obviously, the "salting out" effect cannot well be ascribed to 
some property peculiar to electrolytes alone. 

In a few instances, the addition of a salt causes a marked increase 
in the solubility of a non-electrolyte. This is the case with ether in 
water in the presence of sodium salts of aromatic acids.^* While the 
salts of the aliphatic acids cause a marked depression in the solubili^ 
those of the aromatic acids cause an increase in solubility. 

In Table XCVIII are given values of the equivalent percentage solu- 
bility increase of ether in water due to the addition of 0.5 N salts of 
different acids. 

TABLE XCVIII. 

Solubility Constants for Ether in the Presence of Sodium Salts 

OF Aromatic Acids. 

Solubility 
Salt Solubility Coefficient 

0.5 N Sodium Phthalate 5.88 1.5 

0.5 N Sodium Cinnamate 6.29 15.0 

0.5 N Sodium Benzoate 5.99 4.8 

0.5 N Sodium Salicylate 6.44 20.0 

0.5 N Sodium Benzenesulphonate 6.05 7.0 

The solubility of ether is given in the second column. The solu- 
bility of ether in pure water is 5.85 grams per 100 grams of water at 28°. 
It is evident that the so-called "salting out" effect is not a property 
characteristic of all electrolytes. 

It is of interest to examine the solubility effects in non-aqueous solu- 
tions. Here the data are very meager. Thorin^" has measured the 
solubility of phenylthiourea in ethyl alcohol at 28°. The results are 

TABLE XCIX. • 

Solubility of Phenylthiourea in Ethyl Alcohol in the Presence 

OF Electrolytes. 

Electrolyte Concentration Solubility B' 

LiCl 0.168 norm. 0.2274 norm. 60 

" 0.337 0.2360 42 

" 0.673 0.2440 27 

" 1.346 0.2494 15 

"Thorin. Ztschr. /. phya. Chem. 89, 688 (1915). 
"Tbtd., 89, 691 (1915). 



HETEROGENEOUS EQUILIBRIA 251 

TABLE XCIX.— Continued 

Electrolyte Concentration Solubility B' 

CaClj 0.061 0.2101 28 

" 0.122 0.2135 28 

" 0.244 0.2194 25 

" 0.487 0.2279 21 

" 0:975 0.2372 15 

NaJ 0.043 0.2102 42 

" 0.086 0.2148 46 

" 0.172 0.2198 37 

" 0.343 0.2271 29 

" 0.685 0.2359 21 

NaBr 0.022 0.2098 73 

" 0.043 0.2194 66 

" 0.086 0.2165 57 

" 0.172 0.2257 54 

given in Table XCIX. The solubility in pure alcohol is 0.2065 grams 
per hundred grams of solvent. The equivalent percentage solubility in- 
crease is given in the last column under B'. 

It will be observed that the solubility coefficient is initially quite 
large and decreases markedly at the higher concentrations. The solu- 
bility is in all cases increased, but, as in the case of aqueous solution, the 
solubility effect is a property of the electrolyte in question. The effect 
is greatest for lithium chloride, in which case the solubility is increased 
approximately 20 per cent in a normal solution of the electrolyte. 

Some writers have ascribed the depression of the solubility of non- 
electrolytes in water, due to electrolytes, to the action of the ions 
upon the non-electrolyte. If any interaction of this kind actually takes 
place, it must be of a secondary nature, and greatly qualified by the 
nature of the ions with which the charges are associated. The increase 
in the solubility of phenylthiourea in alcohol clearly indicates that the 
action of the salt upon the non-electrolyte is greatly affected by the 
nature of the solvent medium. Further experimental data on the effects 
of salts on the solubility of non-electrolytes in non-aqueous solutions are 
of much interest. 

4. Solubility of Salts in the Presence of Non-Electrolytes. The 
solubility of salts in aqueous solutions is in general depressed by the 
addition of non-electrolytes. The solubility change, as a rule, follows 
very nearly, although not quite, a linear relation. In the following table 
are given values for the solubility of lithium carbonate in water at 25° in 



252 PROPERTIES OP ELECTRICALLY CONDUCTING SYSTEMS 

the presence of various non-electrolytes, at different concentrations.^" 
The solubility of lithium carbonate in pure water is 0.1687 equivalents 
per liter. 

TABLE C. 

Solubility of Lithium Carbonate in the Presence of 
Non-Electrolytes. 

Mols of non-electrolyte Vs- Vir V2- 1-norm. 

1. Methyl alcohol 0.1604 0.1529 0.1394' 

2. Ethyl alcohol 0.1614 0.1555 0.1417 0.1203 

3. Propyl alcohol 0.1604 0.1524 0.1380 0.1097 

4. Amyl alcohol (tertiary) . . 0.1564 0.1442 0.1224 0.0899 

5. Acetone 0.1600 0.1515 0.1366 0.1104 

6. Ether 0.1580 0.1476 0.1300 

7. Formaldehyde 0.1668 0.1653 0.1606 0.1531 

8. Glycol 0.1660 0.1629 0.1565 0.1472 

9. Glycerine 0.1670 0.1647 0.1613 0.1532 

10. Mannite 0.1705 0.1737 0.1778 

11. Grape sugar 0.1702 0.1728 0.1752 0.1778 

12. Cane sugar 0.1693 0.1689 0.1661 0.1557 

13. Urea 0.1686 0.1673 0.1643 0.1605 

14. Thiourea 0.1667 0.1643 0.1600 0.1523 

15. Dimethylpyrone 0.1562 0.1460 0.1284 0.0992 

16. Ammonia 0.1653 0.1630 0.1577 0.1466 

17. Diethylamine 0.1589 0.1481 0.1283 0.0937 

18. Pyridine 0.1592 0.1503 0.1347 0.1091 

19. Piperidine 0.1584 0.1488 0.1320 0.1009 

20. Urethane 0.1604 0.1525 0.1377 0.1113 

21. Acetamide 0.1614 0.1520 0.1358 

22. Acetonitrile 0.1618 0.1556 0.1429 0.1178 

23. Mercuric cyanide 0.1697 0.1704 

It will be observed that, with a few exceptions, of which mannite and 
grape sugar are the most striking examples, the solubility is depressed by 
the addition of non-electrolytes. In general, the depression is the greater 
the smaller the dielectric constant of the added non-electrolyte, although 
this relation does not hold exactly, since, for example, the addition of 
ether causes a smaller decrease in the solubility than does that of amyl 
alcohol. With increasing complexity of the carbon group the depression 
of the solubility, in general, increases. The solubilities may be expressed 
approximately as a function of concentration by Equation 63. 

In the following table are given the values of 100 P for solutions of a 
number of salts in water in the presence of non-electrolytes." The non- 

=» Rothmund, Ztachr. f. phys. Chem. 69. 531 (1909) 
"Rothmund, loo. cit. 



HETEROGENEOUS EQUILIBRIA 



253 



TABLE CI. 



Solubility of LiCO. 



3, Ag,SO„ KBrOs 
THE Presence of 



KCIO,, Sr(OH)2.8H,0 at 25° in 
Electrolytes. 



Values of 100 |3. 



Li.C03 Ag,S04 
Amyl alcohol (tert.) . . 63.0 54.2 

Dimethylpyrone 56.1 

Ether 52.4 52.2 

Dimethylpyrone 54.6 42.7 

Piperidine 50.5 

Formaldehyde (9.5) 32 4 

Methylal 53.1 

Propyl alcohol 41.7 40.4 

Pyridine 44.4 

, Methylacetate 46.5 

Acetonitrile 34.6 (— 134.8) 

Ethyl alcohol 33.6 31.9 

Chloral 27.9 

Acetone 42.4 39,1 

Phenol (—70.0) 

Cane sugar (50) (—1.5) 

Urethane 41.0 36.7 

Methyl alcohol 19.3 22.1 

Acetamide 20.8 10.7 

Ammonia 14.0 

Glycol 14.2 10.3 

Thiourea 10.3 

Glycerine 9.3 3.4 

Mannite ( — 10.5) (— 20.3) 

Acetic acid 12.3 

Grape sugar (—6.6) (— 11.6) 

Formamide ( — 2.2) 

Urea 4.5 (— 25.3) 

Glycocoll (— 96.3) 



KBrOa 

44.3 
43.8 
38.1 

37.6 
37.1 
33.1 
31.2 
28.3 
25.9 

24.9 

23.5 
23.0 
20.7 
18.7 
14.7 
14.4 
14.3 
10.3 

11.6 
11.6 
9.4 
6.3 
1.1 
0.0 
-9.4 



KCIO, Sr(OH)2.8H20 
28.5 54.1 

19.3 71.0 

19.8 51.3 



10.5 
18.7 

9.0 

6.4 

10.8 

3.3 
16.0 

10.5 
10.1 

3.8 

0.1 

8.2 (- 



32.6 
36.7 



22.8 
37.5 

3.4 

12.3 
19.9) 



9.8 (—54.3) 
•• (—174) 
1.5 



-8.5 
•4.7 



3.6 



electrolytes are arranged vertically in the order of their effect on the 
solubility of potassium bromate. Those values which appear in paren- 
theses in the table are such in which interaction between the non-electro- 
lyte and the electrolyte probably occurs. A negative value of the solu- 
bility coefficient indicates an increase in the solubility. With the possible 
exception of potassium bromate in the presence of glycocoll and potas- 
sium perchlorate in the presence of formamide and urea, the increased 
solubilities are probably to be ascribed to interaction between the elec- 
trolyte and the non-electrolyte. 



254 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

For lithium carbonate, silver sulphate, potassium bromate, and potas- 
sium perchlorate, there is a rough parallelism in the order of the solu- 
bility effects among the different electrolytes in the presence of a non- 
electrolyte, although numerous exceptions occur, particularly in the case 
of lithium carbonate. So, also, the solubility effect in general decreases 
in the order lithium carbonate, silver sulphate, potassium bromate, potas- 
sium perchlorate, although here, again, exceptions are found. There can 
be no question, however, that a parallelism exists between the solubility 
effects for different salts and for different electrolytes. Roughly, those 
non-electrolytes which suffer the greatest solubility change on the addi- 
tion of a non-electrolyte cause the greatest change in the solubility of a 
given electrolyte, and those electrolytes which cause the greatest change 
in the solubility of a given non-electrolyte suffer the greatest solubility 
change on the addition of a given non-electrolyte. These relations, how- 
ever, are only roughly true. It is again evident that the effect of different 
non-electrolytes on the solubility of electrolytes is primarily a function 
of the nature of the electrolyte and of the added non-electrolyte. Similar 
measurements on the solubility effects in non-aqueous solvents do not 
exist. 

5. Solubility of Electrolytes in the Presence of Other Electrolytes. 
If an electrolyte is added to a solution of another electrolyte, which is 
present as a solid phase in equilibrium with its solution, the solubility 
effect will obviously depend upon the interaction between the two elec- 
trolytes. Since electrolytes in solution are ionized and equilibrium estab- 
lishes itself almost instantaneously, it is to be expected that various 
effects will be observed. We have to consider here two cases which are 
of practical importance: First, the solubility of an electrolyte in the pres- 
ence of another electrolyte with a common ion; and, second, the solubility 
of an electrolyte in the presence of another electrolyte without a com- 
mon ion. 

a. Solubility of Weak Electrolytes in the Presence of Strong Electro- 
lytes with an Ion in Common. If the law of mass-action is applicable, 
the addition of a binary electrolyte to a second binary electrolyte having 
an ion in common should cause a depression in the solubility of the second 
electrolyte. We have the equations: 

s -^' 

u 

m: X x,-_ 



HETEROGENEOUS EQUILIBRIA 255 

it being assumed that the two electrolytes have a negatives ion X' in 
common. Here, S^ is the concentration of the un-ionized fraction of the 

first electrolyte, which is assumed to be present in excess, so that there 
exists an equilibrium between the solid salt M^X^ and the solution. If 
the laws of ideal solutions hold, the concentration S„ of the un-ionized 

fraction of the first salt should remain constant. The total concentra- 
tion S of the first salt is then given by the equation: 

(65) S = M* + S^,. 

If a second electrolyte with a common ion Z^ is added, then, in the mix- 
ture, we have the equilibrium expressed by the equation: 

(66) Mimp^Ml)^^^^ 

where M^* + M^* is the concentration of the common ion X', which we 
may write 2C^-. It follows from Equation 66 that: 

(67) ""'^Wf 

and substituting for this value in Equation 65, we have for the solubility 
the expression: 

KiS 

(68) S = S^+-^, 

I 

An examination of this equation shows that the addition of an electrolyte 
with a common ion reduces the solubility of the first electrolyte. If we 
plot values of S as ordinates and those of 2C • as abscissas, the resulting 

curve will be a rectangular hyperbola, whose axis is raised above the 
origin by the distance S . As the concentration of the added electrolyte, 

and consequently the concentration of the common ion, is increased 
indefinitely, the solubility approaches the value S^^ as a limit. The rep- 
resentation of solubility results is greatly simplified if the solubility is 
plotted against the reciprocal of the common ion concentration, in which 
case a linear curve obviously results. This curve ends in a point 



256 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

where So is the solubility of the first electrolyte in pure water and Mox" 
is the ion concentration in this solution. As the reciprocal of the total 
ion concentration, 1/2C-, or the common ion dilution 2F^, decreases, the 

solubility decreases as a linear function of this variable, approaching the 
value S = S^ at 1/2C^ = 0. 

If S, is a constant, as it is if the laws of ideal solutions hold, and if 
if I is a constant, then it follows from Equation 66 that 

(69) M,- X X- = K,S^ = K, 

where X~ is the concentration of the common ion in the solution, and K 
is a constant. For an electrolyte in solution in equilibrium with its 
solid phase, the product of the concentrations of the ions remains con- 
stant, provided that the laws of dilute solutions hold. According to these 
considerations, the solubility of a given electrolyte may be depressed to a 
value which corresponds to the concentration of the un-ionized fraction 
in a solution of the pure electrolyte in equilibrium with its solid phase. 

The foregoing relations are based on the assumption that the laws 
of dilute solutions are applicable. As we have seen, this condition is not 
fulfilled in solutions of strong electrolytes. The effect of the presence 
of strong electrolytes upon the solubility of other strong or weak elec- 
trolytes can, therefore, be determined by experiment only.^*^ The con- 
centration of the various molecular species in the mixture cannot be deter- 
mined, even though the solubility of the first electrolyte is known, unless 
a law is assumed governing the equilibrium of the various electrolytes 
present in the mixture; and the results obtained for the concentration of 
the ionized and the un-ionized- fraction of the first salt in the mixture, 
as calculated, will depend upon the laws assumed as governing the equi- 
librium in the mixture. 

We shall first examine the effect of strong and weak electrolytes upon 

the solubility of weak electrolytes; that is, electrolytes which conform 

to the simple mass-action law. Such determinations have been made by 
Kendall.22 

In Table CII is given values for the solubility of a number of weak 
acids in the presence of other acids, both weak and strong. 

The results are shown graphically in Figures 49 and 50. Considering 
first the solubility of orthonitrobenzoic acid and salicylic acid in the 

"« It Is evident from Equation 69 that K^ and S„ miglit vary In bucIi a manner that 
their product would remain constant, In which case the ion product would remain con- 
^*^''*.; T^" l^J^W improbable, however, that such a compensation actually occurs 

"Kendall, Proo. Roy. Soc. 85 A, 218 (1911). ^ "i-luib. 



HETEROGENEOUS EQUILIBRIA 
TABLE CII. 



257 



Solubility of Weak Acids in the Presence of Other Acids. 
A. Salicylic Acid in the Presence of Formic Acid. 



Formic acid, 
per cent. 

0.00 
0.24 
0.46 
0.625 
1.25 
2.5 
5.0 
10.0 



Solubility, 

gravimetric, 

mols per liter. 

0.01631 



0.01484 
0.01496 
0.01536 
0.01716 
0.02101 



Solubility, 

volumetric, 

mols per liter. 

0.01634 
0.01531 
0.01474 



B. 



Solubility of Hippuric Acid in the Presence of Formic Acid. 



Formic acid, 
per cent. 

0.00 
1.25 
2.5 
5.0 
10.0 



Solubility, 

gravimetric, 

mols per liter. 

0.02045 
0.02014 
0.02078 
0.02275 
0.02661 



Solubility, 

volumetric, 

mols per liter. 

0.02048 



C. Solubility of Salicylic Acid in the Presence of Acetic Acid. 

Acetic acid. Solubility, gravimetric, 

per cent. mols per liter. 

0.00 0.01631 

0.625 0.01691 

1.25 0.01745 

2.5 0.01846 

5.0 0.02059 

D. Solubility of Salicylic Acid in the Presence of Hydrochloric Acid. 



ydrochloric 


Solubility, 


Solubility, 


a,cid. 


gravimetric, 


volumetric, 


normal. 


mols per liter. 


mols per liter 





0.01631 


0.01634 


0.0179 


■ • ■ ■ 


0.01290 


0.0357 


■ > • • 


0.01238 


0.125 


0.01214 





0.25 


0.01194 


.... 


0.5 


0.01123 


• • ■ . 



258 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



E. 



TABLE Cll.— Continued 

Solubility of o-Nitrobenzoic Acid in the Presence of 
Hydrochloric Acid. 



Hydrchloric 


Solubility, 


Solubility, 


acid, 


gravimetric. 


volumetric, 


normal. 


mols per liter. 


mols per liter 




0.04320 


0.04360 


0.0179 


■ • ■ • 


0.03681 


0.0357 


■ ■ > • 


0.03390 


0.125 


0.02980 


. . . ■ 


0.25 


0.02922 


.... 


0.5 


0.02846 


.... 



presence of hydrochloric acid, it will be observed that the solubility de- 
creases greatly on the initial addition of hydrochloric acid, after which 
the solubility decreases slightly, practically as a linear function of the 
concentration. In the presence of the weaker acids, the initial decrease 



0.04 



0.03 



2. o.oz 

o 
w. 



a.oi 



o.co 



V 


0-NtTBOB£NZOC Aoo \H HCl 




V 


Saloi-k: Acid rN HCl 







0.0 



0.1 O.Z 0.3 

Concentration of Added Acid. 



<?.-f 



a.s 



Fig. 



49. Solubility of Moderately Strong Organic Acids in Water in the Presence 
of Hydrochloric Acid at 25°. 

is relatively slight, and this decrease is the smaller the weaker the added 
acid. The solubility of salicylic acid in the presence of acetic acid 
increases from the beginning. In the case of the organic acids the solu- 
bility eventually increases, practically as a linear function of the con- 
centration of the added acid. The results are in harmony with the 



HETEROGENEOUS EQUILIBRIA 



259 



assumption that the initial depression in the solubility of the acid is due 
to the depression of its ionization. Acetic acid is so weak that, even at 
fairly high concentrations, it has no appreciable effect on the ionization 
of salicylic acid, and consequently the resulting curve merely measures 
the increase in the solubility of the un-ionized fraction. In the case of 
hippuric and salicylic acids in formic acid, the added acid is sufficiently 
strong to practically completely repress the ionization of salicylic acid 
present in solution. In these cases, therefore, there is an initial decrease 
in the solubility, while finally, when the ionization is completely repressed, 
the solubility is increased, owing, presumably, to the increased solubility 
of the un-ionized molecules of the first acid on addition of the second. 
By extrapolating the linear solubility curves backwards, until they inter- 

Per Cent of Added Acid. 



o.ozs 




Fig. 50. Solubility of Weak Organic Acids in Water in the Presence of Other 

Organic Acids at 25°. 

sect the axis of solubility, the intercepts on this axis correspond approxi- 
mately to the solubility of the un-ionized fraction in pure water. 

It will be noted that the solubility of salicylic acid and of orthonitro- 
benzoic acid is depressed according to the requirements of the mass-action 
law not only on addition of weak acids, but also on addition of hydro- 
chloric acid. In this case, the solubility of the un-ionized fraction in the 
more concentrated solutions decreases slightly with increasing concen- 
tration of hydrochloric acid. The initial depression effect is marked, 
particularly in the case of orthonitrobenzoic acid, which is a fairly soluble 
acid. Apparently, the addition of a strong acid to a solution of a weak 
acid, as well as the addition of a weak acid to a solution of a weak acid, 
does not greatly alter the ionization constant of weak acids. The ioniza- 
tion constant of salicylic acid at 25° is 1.02 X 10''; that of hippuric acid 
is 2.22 X 10'*; and orthonitrobenzoic add 6.16 X 10"^ 



260 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Kendall and Andrews ^'^ have recently extended the investigation of 
the solubility of acids in the presence of weak acids. They have meas- 
ured the solubility of acids of varying strength and solubility in the 
presence of both strong and weak acids up to high concentrations. They 
include hydrogen sulphide, carbonic acid, boric, oxalic, succinic, trichloro- 
acetic, m-nitrobenzoic, 3-5-dinitrobenzoic, benzoic, picric and P-naph- 
thalene sulphonic acids in the presence of hydrochloric acid; and suberic, 
mandelic, succinic, oxalic, tartaric and boric acids in the presence of 
acetic acids up to concentrations of 10 normal added acid. They have 
also measured the solubility of boric, benzoic and salicylic acids in the 
presence of nitric acid. 

The solubility of all acids on addition of a strong acid is initially 
decreased. On addition of larger amounts of the strong acid the solu- 
bility, with a few exceptions, passes through a minimum. At high con- 
centrations of the added acid, the solubility increase is very marked in 
some cases while, in a few, the minimum is lacking. The initial decrease 
appears to be due to a repression of the ionization of "the saturating acid. 
The stronger the acid, the greater is the initial depression, while in the 
case of very weak acids the initial depression is wanting. The minimum 
solubility of an acid is much lower than corresponds to the concentration 
of its un-ionized molecules in pure water. This is ascribed to the depres- 
sion of the solubility because of hydration effects accompanying the addi- 
tion of the strong acid. It may be noted that the maximum depression 
of hydrogen sulphide and carbonic acids is very low, amounting to only 
a few per cent. The final rise in the solubility curve is ascribed to the 
formation of compounds between the two acids at high concentrations. 
This view is supported by the results of conductance measurements which 
indicate the formation of complexes. This accounts for the widely 
divergent effect of strong acids on different weak acids at higher concen- 
trations. The solubility curves for weak acids in the presence of acetic 
acid exhibit a great variety of form. Here, the common ion effects at 
low concentration of added acid are approximately as might be expected. 

The effect of strong and weak acids on the un-ionized fraction of weak 
acids does not differ greatly from that observed in the case of non-elec- 
trolytes. For example, the solubility of hydrogen in water is only very 
slightly depressed due to the addition of acetic acid, but somewhat more 
strongly due to the addition of hydrochloric acid. In a normal solution 
of hydrochloric acid, the solubility depression in the case of hydrogen is 
7 per cent and that in the case of the undissociated fraction of orthonitro- 
benzoic acid 10 per cent. The percentage depression in the case of sali- 

»" Kendall and Andrews, J. Am. Cltept. Soc. J/S, 1545 (1981). 



HETEROGENEOUS EQUILIBRIA 261 

cylic acid is considerably greater. It appears, therefore, that, on the 
addition of an electrolyte, so far as the solubility relations are concerned, 
substances with polar molecules are affected in the same way as are those 
with non-polar molecules. With polar substances, the same specific 
effects are found which are characteristic of non-polar substances. At 
high concentrations of the added acid, the specific nature of the effects 
indicates some manner of interaction between the two acids. 

b. The Solubility of Strong Binary Electrolytes in the Presence of 
Other Strong Electrolytes. The solubility of a strong electrolyte is, in 
general, depressed on the addition of another strong electrolyte having a 
common ion. On the addition of a salt without a common ion, the 
solubility is in general increased, presumably owing to the formation of 
un-ionized molecules as a consequence of a metathetic reaction. The 
relations are much simpler with binary electrolytes than with electrolytes 
of higher type. The solubility relations are also greatly affected by the 
concentration of the electrolyte, whose solubility is under consideration. 

In Table CIII are given values for the solubility of thallous chloride 
in water at 25° in the presence of various electrolytes.^^ The results are 

TABLE CIII. 

Solubility of Thallous Chloride in the Presence of Other 

Electrolytes. 

Cone, of 
added salt HCl KCl BaCl^ TINO3 Tl.SO, KNO3 K^SO, 

' 10 16.07 16.07 16.07 16.07 16.07 16.07 16.07 

20 10.34 17.16 17.79 

25 8.66 8.69 8.98 8.80 

50 5.83 5.90 6.18 6.24 6.77 18.26 19.42 

100 3.83 3.96 4.16 4.22 4.68 19.61 21.37 

200 2.53 2.68 2.82 

300 .. •• •• .. 23.13 26.00 

1000 •• •• •• •• 30.72 34.16 

shown graphically in Figure 51. An examination of the table and the 
figure shows that the solubility change in the case of different electro- 
lytes is of the same order of magnitude for salts of the same type. The 
depression due to the addition of hydrochloric acid is slightly greater 
than that due to potassium chloride or thallous nitrate. Ternary salts, 
having an ion in common with thallous chloride, cause a depression which 
is very nearly the same as that of binary salts. The solubility is 
markedly increased due to the addition of salts without a common ion. 
While the solubilities due to the addition of different salts differ, this 

»Bray and WinnlnghofE, J. Am. Chem. Soo. S3, 1671 (1911). 



262 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



difference is in general much smaller than in the case of solutions of non- 
electrolytes. 

It is not possible to determine the concentration of the un-ionized 
fraction in mixtures of electrolytes without assuming a law governing 




O.OO 0.02 OO*- C.Oe 0,0S O.IO O.ta 0,/« gjg 

Concentration of Added Salt in Equivalents per Liter. 
Pig. 51. Solubility of Thallous Chloride in Water in the Presence of Other 

Electrolytes. 

the ionization of electrolytes in mixtures. As a rule, the iso-ionic prin- 
ciple has been employed for this purpose. In Table CIV are given values 
for the concentration of the un-ionized fraction, TlCl, and the ion product, 
T1+ X Ch, for solutions of thallous chloride in the presence of different 
electrolytes at 25° ^*, the isohydric principle being assumed to hold for 
the mixtures. 

TABLE CIV. 

Calculated Values of the Ion Phoduct and the Concentration of 

THE Un-ionized Fraction for Thallous Chloride in Water 

AT 25° in the Presence of Different Electrolytes. 



Added Salt 
1/2K,S0, 

1/2T1,S0, 



KNO 



Cone. 

(TlCl 1.755 

|T1+XG1- .... 204.9 

(TlCl 1.755 

|T1+XC1- .... 204.9 

iTlCl 1.755 



|T1- 



KCl 



xci- .... 

Cone. 

JTICI 

(Tl^XCl- .... 

"' Bray and Winnlnghoff, loo. cit. 



204.9 


1.755 
204.9 



20 
1.338 
211.0 
1.465 
208.1 
1:343 
217.4 

20 



25 



25 

1.390 
218.1 



50 

1.120 
218.3 
1.239 
215.7 
1.124 
229.1 

50 

1.204 
229.6 



100 
0.966 
229.7 
1.087 
231.3 
0.968 
243.0 

100 

1.061 

256.3 



300 

0.768 

258.6 



0.775 

279.2 

200 

0.94 

290.0 



HETEROGENEOUS EQUILIBRIA 263 

It will be observed that, according to these calculations, the concen-, 
tration of the un-ionized fraction decreases markedly as the concentra- 
tion of the added electrolyte increases. In a 0.3 normal solution of 
potassium sulphate, the calculated concentration is less than one half 
that in pure water. The ion product increases due to the addition of 
the second electrolyte, this increase depending upon the nature of the 
added electrolyte. On the addition of 0.3 N equivalents of potassium 
sulphate, the ion product increases from 204.9 to 258.6. On the addition 
of 0.2 N equivalents of potassium chloride, the ion product increases from 
204.9 to 290.0. The increase in the case of potassium chloride, there- 
fore, is approximately twice that for potassium sulphate. If the assump- 
tions underlying these calculations are correct, the concentration of the 
un-ionized fraction is greatly reduced on the addition of a relatively small 
amount of a second electrolyte. Since it has commonly been assumed 
that the isohydric principle holds for strong electrolytes, many writers 
have accepted as correct the result that the concentration of the un- 
ionized fraction of the salt is greatly depressed on the addition of an 
electrolyte. As was pointed out in a preceding section, the applicability 
of the iso-ionic principle to mixtures of strong electrolytes is doubtful. 
It is doubtful, therefore, that the above values represent correctly the 
state of the solutions in question. 

The solubility depression of the un-ionized fraction is much greater 
than might be expected from the effect of electrolytes upon the solubility 
of non-electrolytes. The solubility depression of hydrogen in water at 
15° for different salts at normal concentration is in the neighborhood of 
20 per cent, that of oxygen in the neighborhood of 30 per cent, and that 
of nitrous oxide in the neighborhood of 20 per cent. The solubility de- 
pression of phenylthiourea at normal concentration of the added salt is 
24 per cent for potassium chloride, 10 per cent for sodium nitrate, and 
for ammonium nitrate there is a solubility increase of 7 per cent. The 
solubility curves, moreover, while not quite linear, are only slightly 
convex toward the axis of concentrations. Furthermore, on the addition 
of hydrochloric acid, the solubility depression of non-electrolytes is rela- 
tively very small. At normal concentration and 25°, it is 7 per cent for 
hydrogen, 6.8 per cent for oxygen, and 4.4 per cent for nitrous oxide. 
From the effect of electrolytes on the solubility of non-electrolytes, it 
must be concluded, not only that the effect varies greatly with the nature 
of the added electrolyte, but, also, that the magnitude of the effect is 
much lower than that derived from the values calculated on the basis of 
the isohydric principle. Furthermore, it follows from the work of Ken- 



264 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

dall,^'* discussed in the preceding section, that even polar molecules, such 
as we have in the weak acids, are affected only to a slight extent by the 
presence of strong acids. The depression of the concentration of the 
un-ionized fraction of a strong electrolyte in equilibrium with its solid 
phase, due to the addition of other electrolytes, has been ascribed to 
interaction between the ions and the un-ionized fraction of the first salt, 
and the salting out effect in the case of non-electrolytes has been cited in 
support of this hypothesis. From the foregoing analysis, however, it 
would appear that the behavior of non-electrolytes, as well as that of 
weak electrolytes, in the presence of strong electrolytes, lends little sup- ' 
port to this hypothesis. On the whole, it appears much more likely that 
the concentration of the un-ionized fraction varies as a function of the 
nature of the added electrolyte, and that, in general, it varies less than 
indicated by the calculated values given above. 

According to the above calculation, the ion product varies consider- 
ably with the concentration of the added electrolyte and depends, to a 
considerable extent, upon the nature of this electrolyte. Observations 
on the solubility of salts in the presence of. other salts indicate that, even 
in the case of strong electrolytes, the ion product remains approximately 
constant on the addition of other electrolytes.^^ It is at once evident 
that if the concentration of the un-ionized fraction is only slightly de- 
creased on the addition of a second electrolyte, the concentration of the 
ions is appreciably smaller than that derived from calculations on the 
basis of the iso-ionic principle. The result is to render the value of the 
ion product approximately constant and independent of the concentration 
of the added electrolyte. 

As we have seen, the conductance of mixtures of hydrochloric acid 
and sodium .chloride, calculated on the assumption that the equilibrium 
in the mixture is governed by the isohydric principle, is not in accord 
with the experimentally determined values. On the other hand, we saw 
that, in the more dilute solutions, the observed values agree very nearly 
with the values calculated on the assumption that in the mixture the equi- 
librium conforms to Equation 52. It is evident that if C remains con- 
stant in the mixture, P^ will likewise remain constant. If, therefore, 
the concentration of the un-ionized fraction of a salt remains constant, 
the ion product should also remain constant according to this principle. 
Assuming this principle to hold, we may calculate values for the con- 
centration of the un-ionized fraction and for the ion product in the case 
of a salt in equilibrium with its solid phase in the presence of a second 

"Kendall, loe. cit. 

"Stieglltz, J. Am. Chem. Soc. SO, 946 (1908). 



HETEROGENEOUS EQUILIBRIA 265 

electrolyte. For thallous chloride in the presence of potassium chloride 
the following results are obtained: 

TABLE CV. 

Value op the Un-ionized Fraction and op the Ion Product for 

Thallous Chloride in Water at 25°, in the Presence of 

Potassium Chloride, Assuming Equation 52. 

C of KCl 25 50 100 200 

S,j 0.001755 0.001746 0.001734 0.001703 0.001586 

P^-XIO* 2.052 2.039 2.011 1.973 1.808 

The calculations are based upon Aq values identical with those of 
Bray and Winninghoff.^' Taking into account the uncertainties in the 
values of Ao, as well as in the values of the solubilities themselves, it 
appears from an inspection of the above table that, assuming the equi- 
librium in the mixture to be governed by Equation 52, the concentration 
of the un-ionized fraction in the mixture, as well as the value of the ion 
product, remains substantially constant up to a concentration of approxi- 
mately 0.1 N potassium chloride. For example, in the presence of 0.1 N 
potassium chloride, the concentration of the un-ionized fraction as cal- 
culated is 0.001703 as against 0.001755 for a solution of thallous chloride 
in water alone. This represents an increase of only 1.9 per cent. Simi- 
larly, the ion product over the same concentration interval varies only 
4 per cent. The increase in the value of the ion product and the de- 
crease in the concentration of the un-ionized fraction of a binary salt, 
on addition of a second electrolyte with a common ion, is therefore 
primarily a consequence of the form of the function assumed as govern- 
ing the equilibrium in the mixture. The manner in which P^ and C^^ vary 
on the addition of a second electrolyte remains uncertain so long as the 
law governing the equilibria in mixtures remains unknown. 

If the value of the ion product and the concentration of the un-ionized 
fraction remain constant, the solubility of the salt is given by the 
equation: 

(70) ^ = ^u+^ 

where S is the solubility of the salt at any concentration, S^ is the con- 
centration of the un-ionized fraction, which is independent of concentra- 
tion 2C • is the concentration of the common ion, and X^ is a constant 

for the mixture whose value may be determined from the ioniza- 

^ Bray and WlnninghoflE, loc. cit. 



266 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



tion function of the pure electrolyte. The value of 2C^- may be 

calculated by means of Equation 52. From Equation 70, it is evident 
that the total solubility of the salt S in the presence of another salt with 
a common ion is a linear function of the reciprocal of the common ion 
1 



concentration 



2C.- 



In Figure 52 are plotted solubility values for TlCl 



o.oia 



O-oie 




C-oaz 



Reciprocal of Total Ion Concentration 

2C' 

Fig. 52. Representing the Solubility of Thallous Chloride as a Function of the 
Reciprocal of the Total Ion Concentration. 

in the presence of thallous sulphate, thallous nitrate, potassium chloride 
and barium chloride. In the case of KCl as added salt, the values of 
2C • have been calculated according to Equation 52. The other values 

of 2C • are those of Bray,^* which are based on the isohydric principle. 

Since the difference in the values of 2C^ as derived by Equations 51 and 

52 is not great, an approximate comparison is afforded by the values 

MBray, J. Am. Chem. Soo. 33, 1674 (1911). 



HETEROGENEOUS EQUILIBRIA 267 

employed. On examination of the figure, it will be seen that, up to a 
concentration of 0.1 N of added salt, the points lie very nearly upon a 
straight line, and, furthermore, that the solubility values due to the 
addition of different electrolytes conform very nearly to the same straight 
line. It cannot be said that Equation 70 actually holds for the mixture; 
nevertheless, the effect of different electrolytes upon the solubility of 
thallous chloride is much more uniform in character when treated in this 
way than when treated according to the isohydric principle. Up to 
0.1 N concentration of added salt, the solubilities differ only a few per 
cent from' the linear relation. 

The conclusion to be drawn, however, is not so much that the ion 
product and the concentration of the un-ionized fraction as calculated 
according to Equation 52 remain constant for a salt in equilibrium with 
its solution as that the values obtained for the concentrations of the 
various molecular species present in the mixture depend upon the law 
assumed to govern the equilibrium in the mixture. The conclusion 
reached by many writers, that the concentration of the un-ionized frac- 
tion decreases greatly with increasing concentration of the added electro- 
lyte,^" is a consequence of the assumption of the isohydric principle as 
a basis for calculating the concentrations of the various molecular species 
present. As was shown by Bray and Hunt,*" the specific conductances 
of mixtures of sodium chloride and hydrochloric acid, calculated on the 
basis of the isohydric principle, are throughout greater than the measured 
ones. It follows, therefore, that the concentrations of the ions as calcu- 
lated according to this assumption are greater than the true ones. Con- 
sequently, the concentration of the un-ionized fraction, which is obtained 
by difference, is obviously found too low. It is not probable that the 
concentration of the un-ionized fraction of an electrolyte in equilibrium 
with its solutions will be entirely unaffected by the addition of other 
electrolytes, since, as we have seen in a preceding section, the solubility 
of non-electrolytes is influenced by the addition of electrolytes. We 
might expect, however, that the change in the concentration of the un- 
ionized fraction would not differ greatly from that of non-electrolytes 
under similar conditions. This conclusion is further borne out by the 
results of Kendall *^ on the solubility of organic acids in the presence of 
other acids. 

In the case of salts which are more soluble, the effect of a second 
electrolyte upon the solubility is, in general, much smaller and, in some 

"Noyes J Am. Chem. Soc. 3S, 1643 (1911) ; Stieglitz, Hid.. SO, 946 (1908) ; Arrhenlus, 
7,iachr t vhvs. Chem. SX, 224 (1899). 
' Zsisiy ina Hunt, J. Am. Chem. Soc. 33, 781 (1911). 
"Kendall, loc. cit. 



268 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

cases, the solubility may even be increased. The solubility of certain 
salts, such as silver chloride,^^^ is greatly increased on addition of an 
electrolyte with a common ion. Since it has been shown that this effect 
is chiefly due to the formation of complex ions, a discussion of these 
systems may be omitted. 

The solubility of binary salts is materially increased on the addition 
of a salt without a common ion. This may be accounted for on the 
assumption that metathetic reaction takes place between the ions of the 
saturating salt and the solvent electrolyte, the increased solubility being 
due to the formation of the corresponding un-ionized molecules. If the 
isohydric principle is assumed to hold for such mixtures, the resulting 
values obtained for the ion product and the concentration of the un- 
ionized salt are found to vary with the concentration of the added elec- 
trolyte in a manner similar to that found in mixtures with a common ion. 
Here again it is not possible to reach a conclusion relative to the nature 
of the processes involved with any considerable degree of certainty. 

c. The Solubility of Salts of Higher Type in the Presence of Other 
Electrolytes. The solubility relations in the case of salts of higher type 

TABLE Cyi. 

Solubility of Silver Sulphate in Water at 25° in the Presence of 

Other Electrolytes. 

Concentration of 

Salt Salt Solubility 

None ., 0.00 53.52 

KNO3 24.914 57.70 

49.774 61.13 

99.87 67.93 

Mg(N03), 24.764 59.44 

49.595 64.32 

99.46 72.70 

AgNOa 24.961 39.09 

49.86 28.45 

99.61 16.96 

K2SO, 25.024 5066 

50.044 49.35 

100.00 48.04 

200.03 48.30 
MgSO, 20.022 52 21 

50.069 50.93 

100.04 49.95 

200.05 49.60 

""Forbes, J. Am. Chem. Soc. SS, 1937 (1911). 



HETEROGENEOUS EQUILIBRIA 



269 



are much more complex than in that of binary salts and the results are 
accordingly more difficult to interpret. A considerable amount of experi- 
mental material exists, much of which is due to Harkins.^^ 

In Table CVI are given values of the solubility of silver sulphate in 
water at 25° in the presence of different electrolytes. The concentrations 
are expressed in millimols, C X 10"^ per liter. The results for this, as 
well as for other ternary salts, are shown graphically in Figure 53. The 



o.oS 

PbCl, 

0.076 

Tl,C.O. 

0.072 
0.06S 
0.064 
0.060 



^H 


0.056 


1 

CD 


Ag,SO. 


o.o5> 
0.048 


"S3 
> 


0.044 


fla(BrO,), 
0.040 




0.03S 


1 




O.0J3 


K 0.028 



0.016 

0.012 

o.ooS 

0.004 
Ba(IO,), 




0.20 



0.0 0.025 0.05 O.IO 

Concentration of added salt in equivalents. 

Fig 53 Solubility of Ternary Electrolytes in Water in the Presence of Other 

Electrolytes. 

results for lead iodate are given in Table CVII and are shown graphically 

in Figure 54. . , x ui u 

An examination of the figures and the data given m the tables shows 
that, in general, electrolytes of the same type have a similar influence 
upon the solubility of a ternary electrolyte. This is particularly true 
"Harklns, J. Am. ahem. Soc. SS, 1807 (19U) ; md.. S8. 2679 (1916). 



270 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



TABLE CVII. 

Solubility of Lead Iodate in Water at 25° 
OK Other Salts. 



Salt 

None . . . 
PbCNOa), 



KNO, 



KIO, 



:- o.ro 



o.oa 



3 



a <?o« 






o 
>> 

S o.oz 

'a 

_3 
CO 



0.00 



Concentration 
Salt 
0.00 
0.1 
1.0 
10.0 
100.0 
500.0 
3000.0 
2.0 
10.0 
50.0 
200.0 
0.05304 . . . 
0.1061 



IN THE Presence 



Solubility 

• 0.1102 
■ 0.087 

0.0411 

0.0185 

0.016 

0.028 

0.150 

• 0.1141 
0.1334 
0.2037 
0.2544 

• 0.0697 
0.0437 







KN03 




























\l 








? 


\ 


^^^ 


^ 

























O.oooz 0.000^ O.Otoe o.oeoe 0.0010 

Concentration of added salt in equivalents. 
Fjq. 54. Solubility of tead Iodate in Water in the Presepge of Other Eleqtrolytes, 



HETEROGENEOUS EQUILIBRIA 271 

at low concentrations. Salts having a univalent ion in common with a 
ternary electrolyte cause an initial depression, which, in many cases, is 
followed by a slight increase in the solubility at higher concentrations. 
This latter effect, furthermore, is greatly influenced by the properties of 
the electrolytes involved. The minimum is particularly pronounced in 
the case of solutions of lead chloride in the presence of lead nitrate. 
Salts which are only very slightly soluble suffer a much greater depres- 
sion of the solubility on the addition of a salt with a common ion than 
do salts of greater solubility. The addition of an electrolyte without a 
common ion in general causes an increase in the solubility of a ternary 
salt. This increase appears to vary considerably with the nature of the 
added electrolyte. In the case of silver sulphate, for example, the in- 
crease in solubility due to the addition of nitric acid is much greater 
than that due to the addition of potassium nitrate. 

In the case of salts whose solubility is high, the effect of an addition 
of various electrolytes depends largely upon the nature of the added salt. 
In Table CVIII are given the solubilities of strontium chloride in water 

TABLE CVIII. 

Solubility of Steontium Chloride in the Presence of Other 
Salts in Water at 25°. 

Equiv. of 
added salt in Sol. equiv. per 

Salt added 1000 g. H,0 1000 g. H,0 

None None 7.034 

Sr(N03)2 0.1372 7.044 

0.5766 7.038 

1.0988 7.030 

3.318 6.956 
SolidSr(N03)2 

NaNO, 0.3621 7.198 

0.5010 7.270 

3.553 7.276 

6.856 6.844 
Solid Sr(N03), 

HNO3 0.1771 7.028 

0.3521 7.034 

1.277 7.034 

HCl 0.1551 6.882 

0.5162 6.502 

1.017 5.996 

2.165 4.864 

9.205 0.530 



272 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 
TABLE CYllL— Continued 

Equiv. of 
added salt in Sol. equiv. per 

Salt added 1000 g. H,0 1000 g. H^O 

HBr 0.06817 6.974 

0.4191 6.696 

0.9716 6.262 

1.154 6.132 

HI 0.1641 6.890 

0.4462 6.650 

0.4126 6.672 

0.7539 6.366 

KI 0.09199 7.034 

0.5401 7.016 

0.6015 7.038 

1.445 6.992 . 

KCl 0.0719 7.016 

0.433 6.950 

0.8576 6.882 

1.594 6.764 

CuCl^ 0.7134 6.812 

2.276 6.352 

KNO3 0.09796 7.122 

0.4755 7.406 

at 25° in the presence of different electrolytes. The results are shown 
graphically in Figure 55. It will be seen from the table and the figure 
that, up to a concentration of 1.0 N, the solubility effects are, in general, 
small. The difference between the effect of salts with and without a com- 
mon ion is not great. The solubility of strontium chloride remains prac- 
tically constant on addition of nitric acid, potassium iodide, and stron- 
tium nitrate. The addition of potassium chloride causes a slight 
decrease in solubility, while that of sodium nitrate causes a slight in- 
crease. The greatest decrease in solubility results from the addition of 
hydrochloric acid, but it is to be noted that hydriodic acid and hydro- 
bromic acid, which do not have an ion in common with strontium chloride, 
cause almost as great a solubility depression as does hydrochloric acid. 
It is clear that, at high concentrations, the solubility effects are not to be 
ascribed primarily to ionic interaction. The relationships between the 
solubility effects resemble those obtained in the case of solutions of non- 
electrolytes in the presence of electrolytes. 

In the Table CIX are given values for the solubility of lanthanum 



HETEROGENEOUS EQUILIBRIA 273 

iodate in the presence of different electrolytes in water at 25°, as meas- 
ured by Harkins and Pearce.^^ The results are shown graphically in 
Figure 56. It will be observed that the solubility of lanthanum iodate 
IS markedly decreased on the addition of a salt with a common univalent 
ion. The addition of a salt with a common trivalent ion causes a slight 
mitial decrease in solubility, followed by an increase at higher concentra- 



o 
bi) 



f. 



S 7. 



.£; ^. 



3 
C 



T3 I* 

a 



-f 



3. 



a 

3 



CO 

O 



_3 
"o 



z. 




I Z 5 'i- 5 b 7 i. 

Equivalents of added salt per 1000 g. water. 

Fig. 55. Solubility of Strontium Chloride in Water in the Presence of Other 

Electrolytes. 



tions. On the addition of a salt without a common ion, there is a 
marked increase in the solubility throughout. 

While the solubility of different salts is in general affected in a 
similar manner on the addition of other salts, provided the solubility is 
relatively low, the interpretation of the experimental results is ren- 
dered uncertain, owing to the fact that the ionization functions for the 
electrolytes in the mixtures are not known. At the same time, it is pos- 
sible that, in the case of salts of higher type, intermediate ions are present 
as a result of which it not only becomes difficult to take into account 

"Harkins and Pcarce, /. Am. Chem. Soo. 38. 2679 (1916). 



274 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



TABLE CIX. 

Solubility of Lanthanum Iodate in Water at 25° in the Presence 
OF Other Electrolytes. 



Salts added 
La(N03)3 ... 



KIO, 



NalO, 



NaNO„ 



La(N03)3.2NH,N0, 



Milli-normal 

cone, salt 

solution 

0.0 

2.0 

5.0 

10.0 

50.0 

100.0 

200.5 

0.0000 
0.0990 
0.4957 
0.9914 
1.9828 

0.0000 
0.0913 
0.4560 
0.9130 
1.8260 
3.6530 
4.5326 
6.7989 

0.0 

25.0 

50.0 

100.0 

200.0 

400.0 

800.0 

1600.0 

3200.0 

0.00 

26.34 

52.68 

105.36 

158.04 

196.83 

393.67 

787.35 

1574.70 



Solubility 
in millimols 

1.0301 
0.8430 
0.7968 
0.7825 
0.8320 
0.9362 
1.1195 

1.0301 
0.9476 
0.8488 
0.7488 
0.5632 

1.0301 
0.9572 
0.8507 
0.7658 
0.6016 
0.2973 
0.2017 
0.1468 

1.0301 
1.3092 
1.4921 
1.7481 
2.0873 
2.4657 
3.2487 
4.3114 
4.5657 

1.0301 
0.9510 
1.0156 
1.1367 
1.2303 
1.3061 
1.6016 
■ 2.0551 
2.8968 



HETEROGENEOUS EQUILIBRIA 



275 



the effect of the intermediate ion, but, in addition, the concentration of 
the intermediate ion cannot be determined with any degree of certainty, 
even in solutions in pure water. Nevertheless, as Harkins has pointed 
out, the solubility curves may be accounted for in a general way on the 
assumption that intermediate ions are present in solutions of electrolytes 
of higher type. 



O.OIZ 



O.Oie. 



" O.oot 

a . 

§ a 
^^ cooe 

fl > 

^■& 



0.00* 



rs O'OOl 



3 

"3 

































,^ 










♦SiS^ 




"^ 










Z' 




^^^ 


/2u- 


-— ■ 










/ 


■0S^ 


■ 














i 



















Fig. 56. 



fi'Ott. 

0.0 0-1 0.1 0.3 0.4 OS o.e o.i o.a o.a 

Concentration of added salt in equivalents per liter. 

Solubility of Lanthanum lodate in Water in the Presence of Other 
Electrolytes. 



It will be suflBcient to consider, here, the solubility of a ternary elec- 
trolyte of the type MXg, which ionizes according to the equation: 

MXa = M+* + X-. 

As we have already seen in connection with the solubility of binary elec- 
trolytes in the presence of other electrolytes, the experimental results 
in the case of fairly dilute solutions are in reasonably good agreement 
with the assumption that the concentration of the un-ionized fraction 
of the salt, as well as the ion product, remains constant on the addition 
of other electrolytes. If a similar assumption is made in the case of a 
ternary electrolyte, it leads to the following equations for the solubility 
of the salt in the presence of an electrolyte with a common univalent ion, 
a common divalent ion, and without a common ion. 
With a common univalent ion, 

(71) -S = MX, + -p^, 

where K is the' ionization constant of the reaction given above. In this 
equation the solubility appears as an explicit function of the concentra- 



276 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tion of the common ion X". In order to determine the concentration of 
the common ion in the mixture, it is obviously necessary to know the 
ionization functions for the various electrolytes concerned. While these 
functions are not known, a fair approximation could probably be obtained 
by assuming one of the functions given in Chapter IX. This would 
necessarily involve the further assumption that intermediate ions are not 

present. 

On the addition of a common divalent ion, the solubility is given by 

the equation: 

(72) S = MX, + [^-^^y, 
while, on the addition of a salt without a common ion, 

(73) s = MX, + ™^+^, 

where K' is the constant of the reaction 

MY2 = M^^ + 2Y-. 

Since different electrolytes of the same type are ionized to practically 
the same extent in water, it follows that, in the mixture containing a 
salt without a common ion, the equivalent concentrations X" and M+* 
will not differ greatly from each other. The first two terms of Equation 
73, therefore, will remain constant on the addition of a salt without a 
common ion. The last term of this equation, however, will obviously 
increase as the concentration of the ion Y", due to the addition of a salt 
NY, increases. It is evident, therefore, that according to this equation 
the solubility of a ternary salt should be increased upon the addition of a 
salt without a common ion. On the other hand, comparing Equations 71 
and 72, it is evident that the addition of a common univalent ion will 
cause a much greater solubility depression than will the addition of a 
common divalent ion, since the concentration of the univalent ion appears 
in the denominator with the exponent 2, while that of the divalent ion 
appears in the denominator with the exponent %. Roughly, this is in 
agreement with observations. As may be seen by reference to Figure 53, 
the addition of a salt with a common univalent ion causes a much greater 
depression than does the addition of a salt with a common divalent ion. 

As we have already seen, the solubility of a binary salt decreases as 
the reciprocal of the concentration of the common ion. 'The solubility 
curve of a binary electrolyte, therefore, should lie intermediate between 



HETEROGENEOUS EQUILIBRIA 277 

that of a ternary electrolyte in the presence of a common univalent ion 
and in that of a common divalent ion. 

Harkins'* has calculated solubility curves on the assumption that 

(74) S"^ {S + C)^ = 1, 

where m and n are the number of ions resultpg from the dissociation, 
while S is the solubility of the salt and C is the concentration of the 
added salt. The curves calculated on these assumptions correspond 
roughly with the observed curves. An exact correspondence is not to be 
expected, since the assumptions made in calculating these curves are 
obviously only roughly fulfilled. 

The equations given above obviously do not account for the form of 
the curves at higher concentrations, particularly for the increase in the 
solubility of a ternary salt on the addition of larger amounts of a salt 
with a common divalent ion. According to Harkins this increase is due 
to the formation of an intermediate ion MX+ according to the reaction: 

M*^ + X- = MX+- 

On this assumption the solubility on the addition of a salt with a com- 
mon univalent ion is given by the equation: 

(75) s = MX, + ^^ + ^^, 

where K^ is the constant resulting from the reaction: 

MX^ + X- = MX,. 

It is evident, from this equation, that, if intermediate ions MX'^ are 
formed, then, on the addition of an electrolyte NX, the solubility depres- 
sion will be smaller than in the case where no intermediate ions are 
formed. From this equation, it follows, also, as may readily be seen 
by differentiating with respect to the concentration of the common ion 
X", that with increasing concentration the solubility must decrease irre- 
spective of the values of the constants K and Ki. 

If a salt of the type MY, is added, the solubility is given by the 
equation: 



(76) S = MX, + (^^^y XM 



Here K2 is the equilibrium constant resulting from the reaction: 

M++ + X- = MX^ 

•« Harkins, loo. cit. 



278 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

It is evident tiiat: 

(77) K = K^K,. 

An inspection of the above equation shows that, owing to the formation 

of the intermediate ion MX*, the value of whose concentration is given 

by the second term of the right-hand member, the solubility is increased 

due to the formation of the intermediate ion. With increasing value of 

M'^*, this term may become sufficiently great to overbalance the effect 

of the last term of the right-hand member. This is more readily seen on 

differentiating Equation 76 with respect to the concentration of the 

common ion M**, which leads to the equation: 

^'"^ dM**~ M**% \2K^ 2M*V' 

The solubility will be a minimum when: 

^'^^^ 2K, ~ 2W*' 

Obviously, the concentration of the common divalent ion M*+ at the 
minimum point of the solubility curve is equal to the equilibrium con- 
stant K^. If this constant is small, then the minimum point will lie at a 
low concentration; whereas, when this constant is large, the minimum 
point will lie at high concentrations. In other words, when K^ is large 
the fraction of salt present in the form of intermediate ions MX* is 
relatively small; whereas when K^ is small this fraction is relatively 
large and the minimum point accordingly appears at low concentrations. 
It may be noted, in this connection, that the solubility curves of lead salts 
exhibit a pronounced minimum at relatively low concentrations. That 
for lead iodate in the presence of lead nitrate is in the neighborhood of 
0.04 N; that for lead chloride in the presence of lead nitrate is at approxi- 
mately the same concentration. Silver sulphate, in the presence of potas- 
sium sulphate, exhibits a minimum in the neighborhood of 0.1 N. Cal- 
cium sulphate exhibits minima in the .neighborhood of 0.15 N in the 
presence of salts with a common SO^"" ion. In the case of salts with a 
common Ca** ion, this minimum does not appear. The difference in the 
behavior of calcium sulphate in the presence of a common positive or 
negative divalent ion may be due to various causes, since in this case 
there is involved the formation of two different types of complexes. 
Considering the behavior of uni-divalent salts, it is evident that those 
salts which exhibit a pronounced tendency to form complexes, such as 
lead salts for example, likewise exhibit a pronounced minimum in the 
solubility curve in the presence of a common divalent ion. 



HETEROGENEOUS EQUILIBRIA 279 

The simple explanation offerpd above must obviously not be pressed 
too far, particularly m the more concentrated solutions. On the addi- 
tion of a salt of the type MY,, there is a possibility that complexes of 
the form MXY may result. In all likelihood, however, at low concen- 
trations, these are not present to a large extent. 

While solutions of highly soluble salts, as well as solutions of non- 
electrolytes, exhibit a great variety of properties which bring out clearly 
the individual characteristics of the various substances involved, in solu- 
tions of difficultly soluble salts, the solubility curves show remarkable 
regularities, indicating that the observed behavior of these solutions lies 
in properties common to electrolytes in general, at these concentrations. 
The solubility effects are readily explained on the assumption that the 
concentration of the un-ionized fraction, as well as the ion product, 
remains substantially constant on the addition of a second electrolyte. 
The great decrease in the concentration of the un-ionized fraction, which 
many investigators have assumed to be correct, is doubtful. It appears 
probable that this result follows from a failure of the applicability of 
the isohydric principle to mixtures of electrolytes. The solubility in- 
crease observed in the case of salts of higher type on the addition of 
salts with a common polyvalent ion makes it appear probable that 
intermediate ions are present in relatively large amounts in solutions of 
salts of higher type at higher concentrations. 

Heterogeneous equilibria from a thermodynamic point of view will 
be discussed in another chapter. 



Chapter XI. 
Other Properties of Electrolytic Solutions. 

1. The Diffusion of Electrolytes. If a concentration gradient exists in 
an electrolytic solution, diffusion will take place. The rate of diffusion 
of an ion is the greater the greater its mobility. However, in view of 
the fact that the ions of an electrolyte are oppositely charged, the dif- 
fusion of these ions will not be independent of one another. Nemst^ 
has derived an expression for the diffusion coeflBcient in dilute solutions 
of electrolytes. The diffusion coefficient is thus given by the equation: 



(80) 



D = 



2UV 
U + V 



XBT, 



in which U and V are the ionic mobilities. If the electrolyte is not 
completely ionized, the neutral molecules also will diffuse, and their rate 
of diffusion will, in general, differ from that of the ions. The diffusion 
coefficient of various electrolytes has been measured by Arrhenius and 
more extended measurements are due to Oholm.^ In Table CX are given 
values for the diffusion coefficients of different electrolytes in water at 18°. 

TABLE CX. 
Diffusion Coefficients of Electrolytes in Water at 18°. 



Cone. 



NaOl 



KOl 



LiCl 



U.UJ. .... 

0.02 .... 


. . . . 1.152 


1.431 


0.980 


0.05 .... 


. . . . 1.139 


1.409 


0.971 


0.10 .... 


. ... 1.117 


1.389 


0.951 


0.20 .... 


. . . . 1.098 


1.367 


0.929 


0.50 .... 


. . . . 1.077 


1.345 


0.919 


1.00 .... 


. . . . 1.070 


1.330 


0.920 


2.00 .... 


. . . > • ■ 


1.320 


0.928 


2.8 


.... 1.064 


1.338 




36 






4.2 . . 




956 


5.5 


. . . . 1.065 





KJ 

1.460 
1.428 
1.412 
1.391 
1.380 
1.372 
1.366 

1.434 



1.549 



HCl 

2.324 
2.285 
2.251 
2.229 
2.202 
2.188 
2.217 



CHsCOOH 

0.930 
0.910 
0.895 
0.884 
0.871 
0.856 
0.833 



NaOH KOH 



1.432 
1.404 
1.386 
1.364 
1.342 
1.310 
1.290 
1.259 



1.903 
1.889 
1.872 
1.854 
1.843 
1.841 
1.855 
1.892 



'Nernst, Ztschr. f. phj/a. Chem. 2, 613 (1888). 

TT , 'S'\?^"^hn^H'ilf-;J- ^^'- ^'^^"^' *"' ^^^ (1905) ; Meddel. ret.-Akad's. Nohelinatitut, 
Vol. S, No. 22 (1911). 

280 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 281 

It will be observed that in the more dilute solutions the diffusion 
coefficient is the greater, the greater the conductance of the electrolyte. 
Thus, at 0.01 normal, the diffusion coefficient of HCl is 2.324, of KOH 
1.903, of KCl 1.460, and of LiCl 1.000. As the concentration 'increases, 
the diffusion coefficient in the more dilute solutions decreases. This may 
be accounted for if we assume that as the concentration increases the 
ionization decreases, and that the diffusion coefficient of the neutral 
molecules is smaller than that of the ions. At higher concentrations the 
influence of viscosity change must be taken into account. In the case 
of most salts, the viscosity increases with increasing concentration, and 
it is to be expected that, owing to this factor, there will be a decrease in 
the diffusion coefficient at higher concentrations. The increase in the 
value of the diffusion coefficient at very high concentrations cannot be 
accounted for in this way. If, however, the ions are hydrated, then it is 
not improbable that at the higher concentrations, where the number of 
salt molecules becomes comparable with that of the number of water 
molecules, the degree of hydration of the ions decreases, as a result of 
which their mobilities may be expected to increase. 

Of particular significance are the results obtained by Arrhenius' 
for the diffusion of electrolytes in the presence of other electrolytes. If 
the diffusing electrolyte has a rapidly and a slowly moving ion, the dif- 
fusion of the rapidly moving ion is hindered, owing to the drag exerted 
upon it by the charge on the more slowly moving ion. If, now, another 
electrolyte is added, the rate of diffusion of the first electrolyte will be in- 
creased, since the diffusion of the oppositely charged ion may be compen- 
sated by the diffusion of another ion in the opposite direction. For exam- 
ple, the diffusion coefficient of a 0.52 N solution of HCl in water at 12° 
is 2.09, while that of the same electrolyte in 3.43 N solution of NH^Cl is 
4.67, and in a 0.375 N solution of KCl 3.89. Evidently, on adding am- 
monium chloride to the hydrochloric acid solution, the rate of diffusion 
is greatly increased due to the fact that the motion of the Ch ions in the 
direction of the concentration gradient is compensated by a motion of the 
NH/ ions in the opposite direction. This phenomenon is quite general, 
as may be seen from Table CXI. 

The influence of the added electrolyte on the diffusion coefficient is 
extremely marked. For example, the addition of 0.028 N KCl to a 1.04 N 
solution of HCl raises the diffusion coefficient from a value of 2.09 to 2.27, 
or approximately ten per cent. Effects such as these afford perhaps the 
strongest grounds we have for believing that electrolytes are ionized. 
On the other hand, they do not enable us to determine to what extent 

"Arrhenlua, Ztschr. f. phyg. Chem. 10, 51 (1892). 



282 



PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 





TABLE CXI. 




5ION Coefficients 


OF Electrolytes in the 


Presence of Ot] 


Electrolytes in Water at 12° 








Diffusion 


Diffusing 


Added 


Coefficient 


Electrolyte 


Electrolyte 


at 12° 


1.04-n HCl 


None 


2.09 


II 


0.67-n NaCl 


3.51 


II 


0.1-n NaCl 


2.50 


II 


0.75-n KCl 


4.22 


(1 


0.25-n KCl 


3.08 


II 


0.085-n KCl 


2.51 


" 


0.028-n KCl 


2.27 


II 


0.75-n BaCl^ 


4.12 


II 


0.085-n BaCla 


2.46 


II 


2-n NH.Cl 


4.50 


II 


0.25-n NH.Cl 


2.99 


0.52-11 HCl 


None 


2.09 


U 


0.042-n KCl 


2.46 


n 


0.375-n KCl 


3.89 


it 


3.43-n NH.Cl 


4.67 


0.55-n HNO3 


None 


1.91 


tl 


0.1-n KNO3 


2.59 


ii 


0.5-n KNO, 


3.70 


(I 


0.5-n NaNOj 


3.39 


0.54-n NaOH 


None 


1.15 


it 


0.25-n NaCl 


1.90 


11 


0.067-n NaCl 


1.51 


n 


0.25-n Na^SOi 


1.80 


II 


1-n NaNO, 


2.20 


it 


1-n NaCjHaO^ 


1.78 


It 


0.2-n NaNOa 


1.80 


tt 


0.2-n NaC^HjOj 


1.60 


tl 


3-n NaCl 


1.98 


II 


1-n NaCl 


2.30 


0.98-n KOH 


None 


1.72 


II 


0.1-n KCl 


1.92 


II 


1-n KCl 


2.57 


0.49-n KOH 


None 


1.70 


II 


0.05-n KNO3 


1.91 


li 


0.5-n KNO3 


2.54 


It 


0.5-n KCl 


2.57 



ionization has taken place in a given solution. These facts, while they 
do not enable us to distinguish between partial and complete ionization, 
supply abundant evidence that salts are ionized to a large extent. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 283 

2. Density of Electrolytic Solutions. According to the ionic theory, 
the properties of dilute solutions of electrolytes are additive functions of 
the concentrations of the ions and of the un-ionized molecules. If n is 
the value of a given property of such solutions and 

(81) Ak = ^X100, 
then: 

(82) Ajt=:^Y + ^(l — Y), 

where Jto is the value of the property at zero concentration, k is its value 
at the concentration C, y is the ionization of the electrolyte at this con- 
centration, and A and B are constants relating to the ions and the un- 
ionized molecules respectively. Ajt is evidently the percentage equivalent 
property change due to the electrolyte at the concentration in question. 
In applying this equation, it is tacitly assumed that the property is inde- 
pendent of any interaction between the ions and the un-ionized molecule, 
otherwise a term should be added involving the concentration and the 
equation would no longer be linear. Equation 82 may evidently be 
written: 

(83) Alt = B + A'y, 
where 

(84) A' = A — B. 

Are is thus a linear function of y, and from the known values of Ait the 
values of y may be obtained. Such additive properties lend themselves 
to a determination of Yj and a comparison with the value of y as derived 
from conductance measurements might be expected to thus serve as a 
check on the correctness of these values. A simpler method of com- 
parison consists in plotting the measured values of Ait against those of y 
as derived from conductance measurements.* If the two methods yield 
concordant values of y, the graph should be a straight line. 

Unfortunately, this method of checking the results of conductance 
measurements is restricted in its application owing to the fact that in 
many cases the value of a given property for the un-ionized fraction does 
not differ appreciably from the sum of those of its constituent ions. This 
appears to be the case, for example, with many of the optical properties 
of electrolytic solutions. 

Many properties of atomic and molecular complexes depend upon the 

« Heydweiller, Ann. d. Phys. ST, 739 (1912) ; ibid., SO, 873 (1909) ; Magie, Physical 
Review 25, 171 (1907). 



284 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

number and the distribution of the charges within these complexes. If 
these complexes are relatively stable, as we know the ion complex to be, 
then the properties of the complexes will be relatively independent of the 
manner in which two or more of them are grouped together. We should 
not, therefore, expect any considerable change in those properties of elec- 
trolytes which depend primarily upon the distribution of the charges on 
the ions; for the ionic complexes exist practically unchanged in the 
un-ionized molecules whatever their state; that is, whether in solution or 
as liquid, solid, or, perhaps, even vapor. Only such properties as depend 
on the field due to the ions may be expected to exhibit a marked differ- 
ence for the ions and the un-ionized molecules. In the un-ionized state 
the two ions form an electrical doublet with a closed field, while in the 
ionized state the field is open. Those properties, therefore, which depend 
upon the field in the immediate neighborhood of the ions should give evi- 
dence of the existence of the ions and of the un-ionized molecules, should 
these molecules be present in solution. 

Foremost among the properties of this class we should expect the den- 
sity of solutions to be included. It is well known that the solution of 
salts in water is accompanied by a marked volume contraction, which is 
the greater the lower the concentration of the solution. According to 
Drude and Nernst,'* a volume change is to be expected as a result of 
the action of the ionic charge on the molecules of the surrounding 
medium. Obviously, other effects may come into play, such as the hydra- 
tion of the ions, etc. 

The density of aqueous solutions has' been studied from this point of 
view by Heydweiller." He found that, with a few exceptions, the density 
change of electrolytic solutions may be represented as a linear function 
of the ionization corresponding to Equation 82. It is true that the pre- 
cision of the density measurements is not always great and often the 
concentration range over which the equation has been tested is not large. 
Then, again, the lowest concentrations up to which the relation has been 
tested is not much below 0.1 N. It is a remarkable fact, however, that 
for a number of electrolytes the density may be expressed as a linear 
function of the ionization over large concentration ranges, as, for example, 
in the case of zinc chloride, calcium chloride and potassium hydroxide. 

The constant B is the equivalent percentage density change due to the 
un-ionized salt. If it be assumed that the un-ionized molecules in the 
solution occupy the same volume as they do in the pure condition as salts, 
then the value of the constant B may be calculated from the known den- 

■ Crude and Nernst, Ztschr. f. phys. Chem. is, 79 (1894). 
• HeydwelUer, loc. cit. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 285 

sity of the salt. In Table CXII are given values of B^, so calculated, 
together with values of B^, as experimentally determined by Heydweiller 
for different salts in water. 

TABLE CXII. 



Comparison of Experimental and Calculated Values of B. 



Salt 



B„ 



B, 



Salt 



B. 



B, 



NHJ 8.38 

NaCl 3.36 

NaNOa 4.88 

KNO3 5.21 

1/2 K^SO^ . ,. 5.73 

KCIO, 6.73 



AgN03 



13.28 



8.55 


LiN03 


. 3.71 


4.02 


3.15 


LiCl 


. 2.06 


2.17 


4.74 


Nal 


. 10.45 


10.77 


5.30 


1/2 Cal, . . . 


. 11.55 


11.70 


5.45 


1/2 BaBr^ . . 


. 11.80 


11.75 


7.00 


1/2 Balj . . . . 


. 15.56 


15.58 


13.04 


1/2 CdNOg . 


. 9.21 


9.15 



From an inspection of the table it appears that the values of B and 

B^ are in remarkably good agreement. The differences probably do not 

exceed the experimental error. The values calculated in this way, how- 
ever, do not in all cases agree as well as those appearing in the above 
table. In the case of salts which show a marked tendency to form 
hydrates, Heydweiller has employed the density of the hydrated salt 
rather than that of the anhydrous salt and has obtained excellent agree- 
ment between the observed and the calculated values of the constant B, 
while in another group of electrolytes the values of B as calculated are 
not in close agreement with those as measured. This is illustrated in the 
following table. 

TABLE CXIII. 



Comparison op Experimental and Calculated Values of B. 



Salt 



B, 



NH.CI 0.42 

NH,Br 4.45 

NH,NO, 2.60 

1/2 NASO, . 2.49 

Lil 9.53 

LiBr 5.84 



Be 

1.83 
5.69 
3.39 
2.87 
10.10 
6.19 



Salt 



B, 



KCl 2.94 

KBr 6.65 

KI 10.56 

KCNS 3.70 



1/2 K^CrO, 



5.83 



RbCl 6.24 

CsCl 10.36 



3.71 
7.48 

11.20 
4.57 
6.16 
7.79 

12.62 



While there is a marked deviation between the values of B as derived 
from the experimental curves and as calculated from the density of these 



286 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

salts, nevertheless, the parallelism existing between the two sets of values 
is unmistakable. 

The constants A are the equivalent percentage density changes due 
to the ions. This property should be an additive one. If this is true, 
the difference in the values of the constant A for salts with a common 
ion should be constant. Heydweiller has calculated the value of the 
constants A for different ions. To illustrate how nearly the additive 
condition is fulfilled by the experimental values of the constants, the fol- 
lowing values are given. Table CXIV-A relates to a series of sodium 
salts and Table CXIV-B to a series of nitrates. In the first column is 
given the symbol of the negative ion of the salt, in the second column the 
experimentally determined value of the constant A, in the third column 
the value of the constant A^ for the anion, and in the last column the 

difference A — A^ =^/e for ^^e cation. In the case of the nitrates 
similar values are given for those salts. 

TABLE CXIV, 

Showing the Additive Nature of A. 

A. Sodium Salts B. Nitrates 

^ \ ^k A A^ Aj^ 

C3H3O, . 4.44 3.04 1.40 H 3.47 — 1.05 4 52 

F 4.56 3.16 1.40 Li 4.20 —0.35 455 

CIO3 .... 7.33 5.95 1.38 Na 5.95 1 38 4 57 

NO3 .... 5.95 4.54 1.41 Ag 14.61 10.02 4 59 

CI 4.38 3.02 1.36 NH, . . . . 3.61 - 0.98 459 

Br 8.08 6.68 1.40 K 6.72 2 10 4 62 

I 11-52 10.27 1.25 Rb 10.75 6^32 4 43 



OH 4.88 3.40 1.48 1/2 Mg . 5.82 1 33 

1/2 SO, 7.09 5.77 1.32 1/2 Zn .. 8.09 3 61 

1/2 CrO, 7.72 6.38 1.34 1/2 Cd . . 9.94 543 



4.49 

4.48 

4.51 

1/2 Cu . . 8.14 3.63 4.51 

4 55 
1/2 Sr . . 8.98 4.38 4^60 
1/2 Ba ..(10.76) 6.54 (4 22) 
1/2 Pb . . 14.87 10.34 4.53 



Mean 1.38 1/2 Ca . . 6.57 2^02 



Mean 4.54 



It will be noted that the values of the constants A^ and Aj^ show remark- 
ably small variations. They thus fulfill the condition of additivity 
Only a few electrolytes, such as magnesium sulphate, sodium' car- 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 287 

bonate, and sulphuric acid, exhibit density changes which do not vary 
as linear functions of the ionization. The cause of the variation in these 
cases is uncertain, but may be due to the formation of complex ions, to 
hydrolysis, etc. 

The volume changes of electrolytic solutions in methyl alcohol have 
likewise been examined.' The results obtained correspond very closely 
with those obtained in the case of aqueous solutions. The density change 
due to ionization, which is obviously equal to the difference A — B, is 
considerably greater in methyl alcohol solutions than it is in water. This 
is not surprising, since the dielectric constant of this solvent is much 
smaller than that of water. We should expect that, if the density change 
is the result of the action of the field due to the charge on the surrounding 
solvent molecules, the density change would be the greater the smaller 
the dielectric constant of the mediiun. 

In order to finally establish the additive nature of the density changes 
of electrolytic solutions, it will be necessary to extend the measurements 
to much lower concentration. Methods exist for measuring the densities 
of dilute solutions with sufficient precision to make it possible to extend 
the measurements to concentrations approaching 10~^ N. Until this is 
done, the results of density measurements must remain more or less in 
doubt. The concordance of the results so far obtained, however, would 
appear to justify further efforts along these lines. 

Some measurements have been made by Rohrs ^ on the density of 
solutions in ethyl alcohol and acetone. The interpretation of the results 
is uncertain owing to the small change in the ionization over the con- 
centration intervals for which measurements were made. 

3. Velocity of Reactions as Affected by the Presence of Ions. The 
speed of many reactions, such as the inversion of sugars and the hydroly- 
sis of esters, for example, is greatly increased on addition of acids. 
Ostwald " showed that the catalytic effect of different acids is the greater 
the stronger the acid. It appeared, at first, that the catalytic effect of the 
acids' provided an independent method for estimating the concentration 
of the hydrogen ions in an acid solution. Further investigations,^" how- 
ever, showed that the catalytic action is likewise dependent upon other 
factors, such as the presence of other substances and especially electro- 
lytes. Thus, the catalytic action due to a strong acid should be reduced 
on the addition of a salt of this acid. While such a reduction takes place 

' Euthenberg, Inaugural Dissertation, Rostock (1913). 

»Bohr8, Ann. d. Phya. S7, 289 (1912). 

'Ostwald, J. prakt. Chem. 28, 449 (1883) ; 29, 385 (1884) ; SI, 307 (1885). 

i» Arrhenius, Ztschr. f. phys. Chem. 5, 1 (1890). 



288 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

in the case of the weaker acids, in that of the stronger acids the catalytic 
action is actually increased. 

It is now commonly accepted that the un-ionized acid molecules, as 
well as the ions themselves, influence the rate of these reactions. Ac- 
cording to this hypothesis, the reaction constant is given by an equation 
of the form: 

(85) K = KiCj^+K^C^, 

where K- and K are the velocity constants for the ions and the un-ion- 

X lb 

ized molecules respectively and Ci and C are the concentrations of the 
ions and the un-ionized molecules. The constant K^ is in general deter- 
mined by adding, to a dilute solution of an acid, a salt of the same acid. 
Under these conditions, the ionization of the acid is practically repressed 
to zero and it is assumed that the residual catalytic action is due entirely 
to the un-ionized acid molecules. The results of many experiments on a 
great variety of reactions are, on the whole, in good accord with this 
hypothesis. It should be noted, however, that the ratio of the constants 
K^ to K- is a function of the strength of the acid, as well as of other 

factors. The weaker the acid, the smaller is, in general, the value of this 
ratio. In the case of the strong acids, the value of this ratio may be 
unity or even greater. 

In the following table are given values of the inversion coefficient for 
aqueous solutions of cane sugar, according to Ostwald, at 25°. The 
concentration of the acids was in all cases 0.5 N and the values given for 
the constants are relative to that of hydrochloric acid taken as unity. 

TABLE CXV. 

Inversion Coefficients foe Different Acids. 

Hydrochloric acid 1.000 Trichloroacetic acid 754 

Nitric acid 1.000 Dichloroacetic acid 0.271 

Chloric acid 1.035 Monochloroacetic acid . . . 0.0484 

Sulphuric acid 0.536 Formic acid 0.0153 

Benzenesulphonic acid 1.044 Acetic acid 0.0040 

It is clear that the catalytic action of the acids is intimately related 
to their strength. 

For the purpose of investigating the effect of the neutral molecules 
upon reactions, solutions in non-aqueous solvents are in many respects 
better adapted than those in water, since the ionization of the acid in 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 289 

these solutions is much smaller than in water. Numerous experiments 
have therefore been carried out in methyl and ethyl alcohols. 

In the following table are given values of the esterification constant 
for different acids in methyl alcohol, according to Goldschmidt and 
Thueson," at 25°. The numerical values for 0.05 HCl, 0.1 picric acid 
and 0.1 trichlorobutyric acid are given in the second, third and fifth 
columns respectively, while in the fourth and sixth columns are given 
the values for picric acid and trichlorobutyric acid of the strength given 
in the presence of 0.15 picrate and 0.1 butyrate respectively. 

TABLE CXVI. 

Esterification Constants in Methyl Alcohol for Different Acids 
IN the Presence of Other Acids as Catalyzers. 

Catalyzing acids 
Esterifying acid HCl CeHsNgO, Picrate C.ClaH.O^ Butyrate 

Phenylacetic acid . . 2.23 0.265 0.047 0.0167 0.00102 

Acetic acid 4.86 0.590 0.100 0.0375 0.00172 

n-Butyric acid 2.23 0.277 0.0535 0.0177 0.00097 

i-Butyric acid 1.55 0.196 0.0353 0.0129 0.00074 

i- Valeric acid 0.583 0.0735 0.00144 0.00475 0.00029 

From this table it may be seen that the catalytic action of an acid 
is the greater the stronger the acid. Nevertheless, the catalytic action 
of an acid is not proportional to the concentration of the hydrogen ion. 
The ratio between the velocity constants for 0.05 N hydrochloric acid 
and 0.1 N picric acid varies between 7.78 and 8.91 for the different acids, 
while the ratio of the ion concentrations is 6.56. So, also, the ratio of 
the hydrogen ion concentrations for 0.1 N and 0.01 N picric acid is 3.64. 
The ratio of the esterification constants between these concentrations is 
3.90. It will be observed that, on the addition of sodium picrate to picric 
acid, the velocity constant varies approximately in the ratio of 1 to 6, 
while, on the addition of trichlorobutyrate to butyric acid, the velocity 
constant changes in the ratio of 1 to 18. It should be stated in this con- 
nection that the values given for the constants of picric acid and tri- 
chlorobutyric acid in the presence of other salts represent practically the 
minimum limiting values which are independent of the concentration of 
the added salt. In other words, the salt added is suflBcient to completely 
repress the ionization of the acid. Accordingly, the residual catalytic 
action of the acid must either be due to the un-ionized molecule or to 
some other agency. The weaker the acid, the smaller, relatively, is the 

"'Goldschmidt and Tiueson, Ztschr. f. phj/s. Chem. 81, 30 (1913). 



290 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

catalytic power of the neutral molecule. The values of the constants 
K- and K may be determined from a series of measurements. In the 

% lb 

case of the examples given above the following values of K^Cj^ were 

obtained for trichlorobutyric acid as catalyzer at concentrations of 0.1 
and 0.05 N. 

TABLE CXVII. 

Velocity Coefficients for the Hydrogen Ion of Trichlorobutyric 
Acid in the Esterification of Different Acids. 

Con- 
centration Phenyl- 
of Acid acetic Acetic n-Butyric i-Butyric i-Valeric 

0.1 0.0157 0.0358 0.0167 0.0122 0.00448 

0.05 0.0109 0.0247 0.0114 0.00826 0.00304 

Ratio .... 1.44 1.45 1.47 1.48 1.47 

It is seen that the ratio of the velocity coefficients calculated for the 
ions between 0.1 and 0.05 N is 1.46. According to conductance measure- 
ments the ratio of the ionization of this acid at these two concentrations 
is 1.42. Taking into account the numerous possible sources of error, the 
agreement appears fairly satisfactory. 

In the following table are given values of K^ and -^^ for hydrochloric 

acid, acetic acid, and the chloro- substitution products of this acid.^^ 

TABLE CXVIII. 

17- 

Varlvtion of the Ratio ~ for Different Acids. 

i 

Acid K — K 

I 

Hydrochloric acid 780 1.77 

Dichloroacetic acid 220 0.50 5.1 X lO"'' 

a-P-Dibromopropionic acid 67 0.152 L67 X 10"" 

Monochloroacetic acid 24.5 0.055 0.155 X 10"" 

Acetic acid 1.5 0.0034 o!o018 X 10"" 

Similar results have been obtained by Taylor and by Ramstedt." It is 
clear that the value of K^ increases with the strength of the acid. As 

,'.'5*^^°° ^^^ Fowls, J. Cliem. Soc. 101,, 2135 (1913). 
Ypl. S,N9 7' (^9%T.^ ^' ^^■•^'""^''- Nvielinstitut, Vol. S, No. 1 (1913) ; Ramsteat, mi.. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 291 

shown in the table, the catalytic action of the neutral molecule of hydro- 
chloric acid is greater than that of the hydrogen ion. As the acids become 
weaker, however, the catalytic activity of the neutral molecule diminishes 
and reaches very low values in the case of weak acids. According to 

Taylor, the ratio -^ is related to the ionization constant of the acid by 
the equation: 

(86, (r:)=^'^- 

where 4 is a constant. If the law of mass action applies to the acid, this 
leads to the relation: 

where C^ and C^ are the concentrations of the un-ionized and the ionized 
fractions of the acid, respectively. 

Many reactions are likewise catalyzed by the hydroxyl ions and, in 
alcohol solutions, by the alcoholate ion.^* Since the results obtained in 
these cases do not differ materially from those obtained in the case of 
acids, the details need not be given here. 

It is evident that the catalytic action of the hydrogen and hydroxyl 
ions may not be safely employed for determining ion concentrations. At 
all events, the interpretation of the results obtained is still very uncertain. 
In this connection, it may be noted that Arrhenius^^ has proposed an 
alternative hypothesis to account for the effect of the vm-ionized fraction 
according to which the change in the catalytic activity is a secondary 
effect due to a change in the osmotic pressure of the molecules as a 
consequence of the addition of the neutral salt. While the catalytic 
effects due to the ions are of great interest and often of much practical 
importance, nevertheless, at the present time, they have not enabled us 
to gain any great insight into the nature of electrolytic solutions. 

Recently a number of investigators have ascribed the effect of neutral 
salts on the catalytic action of strong acids to the influence of the added 
salt on the thermodynamic potential; or, what is equivalent, the activity 
of the hydrogen ion. Harned ^° has studied the action of neutral salts on 
the rate of various reactions which are catalyzed by ionic catalysts and 
has compared this effect with the change in the activity of the catalyzing 

" Acree, numerous articles in the Am. Chem. J. and J. Am. Ohem. Boo. since 1907. 
See: Acree, Am. Ohem. J. 1,9, 474 (1913). 

" Arrheuius and Andersson, Meddel E. Yet.-Ahad's. NobeHnstitut 3, No. 35 (1917), 
'•Harned, J. Am. Chem. Sop. J,0, 1461 (1918), 



292 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ions due to the addition of another salt with a common ion. He finds, 
in general, a correspondence between the two effects. Harned has also 
pointed out that the neutral salt effect appears to be related to the hydra- 
tion of the added salt. 

Akerlof " has measured the influence of acids on the rate of reaction 
of ethyl a«etate in water at 20° in the presence of varying concentrationa 
of salts having an ion in common with the acid. The activity of the 
hydrogen ion in the presence of an added salt was determined by meas- 
urement of the electromotive force of concentration cells. With hydro- 
chloric and sulphvuric acids, Akerlof found that, with increasing activity 
of the hydrogen ion, the velocity constant increases. For the same con- 
centration of the catalyzing acid, the velocity constant K^ was found to 

increase approximately as the cube root of the activity of the hydrogen 
ion; or, 

(87) K^ =Aai, 

where K is the velocity constant of the reaction, .4 is a constant having 

the same value for different salts, and a is the activity of the hydrogen 
ion in the mixture. In the case of a number of salts the value of A was 
found to depend upon the nature of the salt as well as upon its concen- 
tration. It is possible that these discrepancies' are due to various sources 
of error. With increasing acid concentration, the constant A was found 
to increase, but apparently not in direct proportion to the concentration. 

Equation 87 is an empirical one, and, so long as it lacks a theoretical 
foundation, the interpretation of the foregoing results remains uncertain. 
It appears that, for a number of salts, the velocity constant varies in a 
similar manner with the activity of the catalyzing ion; but, in view of 
the possible exceptions which have been found, it would be unsafe to 
generalize the results obtained. Further investigations along this line, 
however, are of considerable interest. 

4. Optical Properties of Electrolytic Solutions. Among the various 
optical properties of solutions, only the absorption spectra have been 
determined with sufficient precision to make it possible to draw conclu- 
sions with any degree of certainty. Since the optical properties are pri- 
marily dependent upon the number and arrangement of the electrons, 
it is not to be expected that the ions and the un-ionized molecules will 
exhibit any marked difference with respect to these properties. It is true 
that, in the case of a few solutions, such as the copper salts for example, 
marked changes take place in the optical properties as the concentration 

"Akerlof, Ztachr. f. phya. Chem. SS, 360 (1921). 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 293 

changes, but these changes are to be ascribed, primarily, to a displace- 
ment of the hydration equilibrium existing in these solutions. As the 
solutions become more dilute, this effect disappears. The absence of any 
difference in the optical effects of the ions and of the un-ionized molecules 
has led some writers to infer that un-ionized molecules are entirely want- 
ing in electrolytes. This inference, however, does not appear to be well 
founded. 

In general, if no reaction "takes place which tends to alter the nature 
of the chromophore group, the absorption of an ion is independent of the 
nature of the solution, as well as that of other ions with which it may be 
combined. This is well illustrated in the case of the absorption of acetic 
acid in the ultra-violet region. 

In Figure 57 is shown the absorption curve for acetic acid " in water 
and in petroleum ether and for the potassium and barium salts of this 
acid in water. From an inspection of the figure it is evident that the 
absorption of these solutions is the same within the limits of experimental 
error. In Figure 58 is shown the absorption curve for ammonium, potas- 
sium, barium and calcium salts of trichloroacetic acid in water.^^ Here, 
again, it is evident that the absorption curves are identical within the 
limits of the experimental error. What holds true in the cases which 
have just been cited holds true also in solutions of other electrolytes. In 
general, whenever a variation arises in the absorption curve, as a result 
of a change in the solvent or a change in the accompanying ion, this 
effect may be ascribed to some reaction taking place in these solutions 
which alters the nature of the chromophore group. 

In the following table are given the extinction coeflBcients for chromic 
acid and potassium bichromate in water according to the measurements 
of Hantzsch.^* 

TABLE CXIX. 

Extinction Coefficients of Chromic Acid and Potassium 

BiCHEOMATE IN WaTEH. 









H,Cr,0, 






KjCr^Oj 




Wave Lengths 


405 


436 


486 


543 


405 


436 


486 


546 




10 


.. 


.. 


, , 


1.9 


• a 


, , 


, , 


1.73 




100 




• • 


89 


1.8 


, , 


291 


88.7 


1.67 


V ■ 


500 


333 


275 


, , 


, , 


, , 


292 


86.8 


• • 




1000 


320 


269 


88.5 




332 


287 


87.2 





"Hantzsch, Ztschr. f. phys. Chem. 86, 629 (1914). 

^* Idem, loc. cit. 

^Idem, Ztschr. f. pTvys. Chem. 63, 370 (1908). 



294 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Wave Length. 



Wave Length. 
3SeO 700 800 900 



o 

o 

d 
o 



J3 



100 










+ 








80 
$3^1 


























SO 




.^^ 








^ 






*0 

3i.e 

25 




























+ 






20 






c 








- 




16 




















n.6 


















10 






?«n 








+ 




8 






x 








+ 




S3 






•>, 


c 


f 








• 



wsfll 



•w^tf 



»tf 



2^0 



Jl^ 



'HiCO 



Fig. 57. Absorption Curve of Tri- 
chloroacetic Acid in Water(. ) and 
in Petroleum Ether (X), and of Po- 
tassium Trichloroacetate in Water 
(+), and Barium Trichloroacetate in 
Water(o) as a Function of the Wave 
Length. 



100 



so 



$3.1 



SO 



*0 



3t 

§ 3 

O 

d 
o 



M 

Xi 

< 



2i 



20 



16 



12.6 



10 



« 


3: 








I 
















V 

+ 








+ 








^ 

^c 








> 








< 


< 
















^0 








4? 

X 








+ 








+ 





Fig. 58. Absorption Curves of Aqueous 
Solutions of NH,(.), K(-|-), Ba(X), 
and Ca(o) Trichloracetates. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 295 

It will be observed, from this table, that the values of the extinction 
coefficients for chromic acid and potassium bichromate are identical 
within the limits of experimental error. The absorption here is due to 
the negative ion. It will be noted that the absorption, moreover, is 
independent of the concentration, which indicates that the negative ion 
in the un-ionized molecules possesses the same optical properties as in its 
free state; that is, in its conducting state. The absorption coefficients of 
the chromate ion are not affected by the presence of acid, but they are 
slightly affected by the presence of bases. In the following table are 
given values of the extinction coefficients for potassium bichromate in 
the presence of varying amounts of potassium hydroxide for the wave 
length l = 486. 

TABLE CXX. 

Absorption Coefficients of Solutions of Potassium Bicheomate in 
THE Presence of Potassium Hydroxide. 

Wave Length I = 486. 

Cone. Base 1/2000 1/100 1/1 

89.9 84.3 83.7 81.7 

89.0 84.0 83.0 82.3 



89.0 83.6 82.0 81.4 

It will be observed that, on the addition of potassium hydroxide, the 
absorption of potassium bichromate is affected to a small but measurable 
extent. Hantzsch has shown that this is due to the formation of other 
chromophore groups. 

In different solvents, the chromates have identical values of the ab- 
sorption coefficients, as may be seen from the following table. 

TABLE CXXI. 

Absorption Coefficients of Sodium Chromate in Methyl 
Alcohol and in Water. 

I = 486. 

V H,0 CH3OH 

2000 229 231 

5000 227 233 

The results obtained from a study of other chromophore groups are 
similar to those obtained in the case of the chromates, and need not be 
given here. 



296 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Hantzsch ^^ has also studied the absorption of salts of certain organic 
chromophore groups. In certain of these salts, marked changes have 
been found and Hantzsch has been able to show that in these cases the 
change is due to a shift in the equilibrium between two chromophore 
groups. In the case of salts of certain organic chromophores, however, 
small differences have been found for which an adequate explanation has 
not thus far been given.^^ In the following table are given values for the 
equivalent extinction coefficients for different salts of acetyloxindon. 

TABLE CXXII. 

Extinction Coefficients fok Different Salts of Acetyloxindon 

IN Water. 

l = 436. 

Concentration: 1/100 1/250 1/1250 1/2500 1/5000 

Thickness of layer: 1 mm. 1 cm. 2 cm. 5 cm. 10 cm. 



Salt^ 



Sr 400 388 390 384 

347 350 358 350 

385 390 382 380 

391 387 380 390 

385 381 390 394 



Li 


Na 


388 


Cs 


383 


Tl 


389 



In aqueous solutions, the absorption spectra of the different salts of this 
acid are very nearly identical with the exception of the lithium salt, 
whose values appear to be a little low. In the case of all salts, the extinc- 
tion coefficient is independent of the concentration. 

While the extinction coefficients for the oxindon salts in aqueous solu- 
tions are the same for all cations, with the possible exception of lithium, 
in solutions in ethyl alcohol a marked difference has been found. In Table 
CXXII are given values of the extinction coefficients of different salts in 
ethyl alcohol. It will be observed that here, again, the value of the co- 
efficient is independent of the concentration, but that it varies with the na- 
ture of the positive ion. This variation is unquestionably far in excess of 
any probable experimental error. The difference might be ascribed to a 
difference in the optical properties of the un-ionized molecules, and it is 
known that in these solutions the ionization of these salts is relatively low. 
However, over the concentration ranges in question, the ionization for a 
given salt varies considerably, which makes it difficult to account for the 
constancy of the coefficient at different concentrations. While Hantzsch is 

"Hantzsch, Ber. iS, 82 (1910). 

"Idem, Ztachr. }. phys. Chem. 8J,, 321 (1913). 



. , 


214 


220 


226 


217 


, , 


230 


227 


232 


231 


, , 


230 


238 


240 


236 


259 


263 


255 


250 


258 


325 


330 


328 


325 


322 


339 


338 


333 


325 


340 


329 


327 


329 


343 


341 


390 


409 


393 


383 


395 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 297 

TABLE CXXIII. 

Extinction Coefficients for Salts of Acetyloxindon at Different 
Concentrations in Ethyl Alcohol. 

X = 436. 

Concentration: 1/100 1/1000 1/1000 1/2500 1/5000 

Thickness: 1cm. 1cm. 2 cm. 5 cm. 10 cm. 

rca 

Sr 

Ba 

Li 

Salt-^Na 

K 

Rb 

Cs 

_T1 325 328 337 330 

inclined to account for these variations on the basis of a slight rearrange- 
ment in the chromophore group, somewhat similar to that established in 
the case of the salts of the oximidoketones, a thoroughly satisfactory ex- 
planation of this behavior of the above solutions does not exist. 

From the foregoing, it appears that, in solutions of salts which have 
stable chromophores, the absorption spectra are independent of the con- 
dition of the salt, and accordingly we may conclude that, whether an ion 
is combined or uncombined, the absorption spectrum remains unchanged. 
Where changes occur, reactions are to be looked for, the nature of which, 
however, has not been established in all cases. 

5. The Electromotive Force of Concentration Cells. The properties 
of a solution are determined by the values of the variables which fix its 
state. If the solution is subject to the action of external forces, its prop- 
erties will vary accordingly. Under such conditions the thermodynamic 
potential of the dissolved substance suffers a change and electromotive 
forces naturally arise under suitable arrangement of solutions and elec- 
trodes. Such, for example, is the case when solutions are subjected to 
centrifugal action.^^ We shall, however, confine ourselves here to a con- 
sideration of electromotive forces arising as a result of concentration dif- 
ference. Wherever we have a surface of discontinuity between two 
electrolytes, or between an electrolyte and a metal, an electromotive 
force will in general arise. 

For a system under the action of external forces, the condition for 

» Tolman, Proc. Am. Acad. iS, 109 (1910). 



298 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

equilibrium requires that the total potential shall be the same throughout 
the system. The total potential is defined by the equation: 

(88) M' = M-\-P, 

where M' is the total potential of a given molecular species, M is its 
thermodynamic potential, and P is the potential due to the external 
forces. The thermodynamic potential may be expressed as a function of 
the concentration by means of the equation: 

(89) M = RT log C + i + J, 

where i is a function independent of concentration, while J is a fimction 
which, in general, involves all the independent variables of the system. 
For a concentration cell operating between the concentrations C^ and 
Cj, we have: 

(90) (M^ + M-)^— (M* + M-)^ = — W, 

where M* and M" are the thermodynamic potentials of the ions of a 
given electrolyte and W is the work performed by the cell when one 
equivalent (or mol) of the electrolyte is carried from the first solution to 
the second. Introducing Equation 89, and writing for W its value in 
electrical units, we have: 

(91) - tEF = ET log ^^_ + (2J.), - (2J^.)i, 

where 2J^- = J+ -f J-. F is the electrochemical equivalent, E the elec- 
tromotive force, and r the number of equivalents of electricity flowing 
per equivalent of electrolyte transferred. The value of r depends upon 
the number of charges v associated with a molecule of the electrolyte 
and the nature of the electrode process. For a concentration cell with 
transference, 

(92) r = v/N, 

where N is the transference number of the ion to which the electrodes 
are impermeable. For cells without transference, N = l. The electro- 
motive force E is that due to the transfer of the electrolyte alone, and, 
if other processes are involved, the measured electromotive force must 
be corrected for these processes before introducing into Equation 91. 
At higher concentrations, in view of the fact that the ions are hydrated, 
solvent will be carried from a solution of one concentration to that of 
another. This process involves work and the electromotive force, as 
measured, must be corrected accordingly. In general, since the relative 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 299 

hydration of the ions is not known at the concentrations in question, 
such corrections cannot be made. The same considerations hold true of 
the reactions in which the electrolyte is concerned, such as the formation 
of intermediate or complex ions, complex molecules, etc. 

The electromotive force of a concentration cell may likewise be 
expressed in terms of the concentrations of the un-ionized fraction, which 
leads to the equation: 

(93) -rEF = RTlog^+J^^-J^^. 

If the conditions of dilute systems are fulfilled, then: 

(94) J- = J- = J^ = 0, 

in which case the electromotive force of the cell may be calculated, if the 
concentration of the ions or of the un-ionized molecules is known. 
Equation 93, in this case, reduces to: 

(95) — rEF = RT log ^''^'' 



This is the equation first developed by Nernst.^* 

When the conditions for a dilute system are no longer fulfilled, the 
fimction J is involved in the expression for the electromotive force. This 
function thus measures the change in the potential of the electrolyte due 
to interaction between the various molecular species present in the 
mixtm-e. The form of this function is not known, except in so far as it 
has been determined experimentally. The electromotive force of concen- 
tration cells has in many cases been employed for this purpose, since 
it affords a convenient and direct measure of the change in the potential 
of the electrolyte. In order to determine the true form of the function, 
however, it is necessary to know the concentrations C* and C" or C . 

Except as the concentration of the ions may be determined from con- 
ductance measurements, no method appears to be available whereby the 
concentrations of the ions and of the un-ionized molecules in an electro- 
lytic solution may be determined. 

For practical purposes, the equation is often written: 

C ^ 
(96) -TEF==BT\og^, + ^J^-^^. 

"Nernst, Ztschr. }. phya. Chem. 2, 613 (1888). 



300 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

If the electromotive forces have been determined experimentally, they 
may be expressed as a function of the total salt concentration C by 

means of this equation. In this case, the function J, includes not only 

the change in the potential of the electrolyte due to the internal forces 
of the system, but it also includes a term which takes into account the 
change in the expression due to the substitution of C„ for C* and C: 

The electromotive force of concentration cells for a great many elec- 
trolytes has been measured by various investigators.^'' Only a few 
examples of the results obtained will be given here to show, in a general 
way, the manner in which the potential of an electrolyte varies with the 
concentration. In Table CXXIV are given values of the electromotive 
force of concentration cells with hydrochloric acid as electrolyte between 
silver chloride electrodes.^* The concentration of the concentrated solu- 
tion is in this case throughout 0.1 N. The concentration of the dilute 
solution is given in the first column, in the second column is given the 
value of the electromotive force as measured, in the third and fourth 

C ■ C 

columns are given the values -^ and -^, as determined from conduc- 

tance measurements, and in the fifth and sixth columns the values of the 
same ratios as calculated from Equations 93 and 96, assuming J = 0. 

TABLE CXXIV. 
Comparison of Values of — ' and — ^ for HCl as Derived from 

Conductance and Electromotive Force Measurements. 

(Cal.) (Cal.) 

(;■ r 

Concentration 
of dilute sol. E.M.F. 
0.02 0.07617 

0.01 0.10913 

0.002 0.18711 

(]. 
It will be observed that the calculated values of the ratio — do not 

differ greatly from those derived from conductance measurements, but 

"Linhart, J. Am. Chem. Soc. S3, 2601 (1917) • ibid i,i 117s mqiqi . mm .^., 
SS, 737 (1916i ; Noyes and Ellis, ibll, as, 2532 (1917) -lewis sLUnii =^^Fk' ^}>^-' 
iUd., S9 22i5 (1917) ; Allmand and PoZ^cfc, 1 ahem ' i^c % i.f20n 5??,^^^^'"*°! 
and Cushman, J. Am. Chem. Soo. to. 393 (191R • TTn?n»/i J..-w »i^'iJ.^i„! Randall 
Loomis, Essex' and Meacham, iM<J.,Vil33 (19i7) • fo^i, fn'rt Jli."/ ^^-fi* (1915) I 
632 (1911) ; Maclnnes and Beattie. / Ami O^em: Soo T 1117 (1920)- ^™- ^"^^ '^- *^' 

"Tolman and Ferguson, J. Am. Chem. Soc si 232 (l'912) ^^^^^>- 





^.1 


4.78 


7.76 


9.49 


17.3 


46.7 


112.5 



% 
% 


^.1 


4.57 


20.9 


8.82 


11.1 


41.8 


1744.0 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 301 

C 
that, on the other hand, the calculated values of the ratio — ' differ 

Q 

enormously from those measured. The value of the ratio y^, as deter- 

mined from conductance measurements, may be somewhat in error 
owing to uncertainties in the value of A^. Since the value of 1 — y is 
relatively small, it is obvious that a small error in the value of Ao 
will have a large effect on the value of the ratio determined from 
conductance measurements. Nevertheless, it is evident that the electro- 
motive force as measured is much greater than that calculated according 
to Equation 95. 

In the case of other electrolytes similar results have been obtained. 

In the following table are given values of -^ as calculated from the 

electromotive force of potassium chloride concentration cells.''' The 
concentrations of the solutions are given in the first two columns, the 
values found and calculated for the ion ratios are given in the last two 
columns. 

TABLE CXXV, 

Comparison of the Ratio y^, as Determined from Electromotive 
Force and Conductance Measubements. 









<^V 


^,- 




C 




^(Cond.) 

^^2 


7^'(Cal.) 


0.5 




0.05 


8.85 


8.09 


0.1 




0.01 


9.16 


8.33 


0.05 




0.005 


9.30 


8.64 


0.01 




0.001 


9.62 


9.04 



It is evident that the ion ratios as determined by means of conductance 
measurements are considerably greater than those calculated from the 
measured electromotive forces, assuming Equation 95 to hold. As the 
solutions become more dilute, the two values approach each other slowly. 
The explanation of these phenomena has been the subject of much 
discussion. The observed fact is that, assuming the laws of dilute 

solutions to hold, the electromotive force of a concentration cell as 

I 

"Maclnues and Parker, J. Am. Chem. Soc. S7, 1445 (1915). 



302 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

measured is smaller than that which would be calculated from the con- 
centrations of the ions and larger than that calculated from the con- 
centrations of the un-ionized fraction. One obvious explanation is that 
the conditions assumed to hold in applying the Nernst equation are 
not fulfilled, for this equation obviously can apply only to solutions 
which are sufficiently dilute so that the deviations from ideal systems 
lie within the experimental error. The behavior of solutions of strong 
electrolytes clearly shows that this condition is not fulfilled. The 
Nernst equation, therefore, should not apply. 

On the other hand, it is possible that the ionization measured by 

means of the conductance ratio -r- is not correct. If this is true, the 

Ao 
concentrations of the ions are not known and it is therefore not possible 
to calculate the electromotive force of a concentration cell from Equa- 
tion 95. In this case, we still have to take account of the fact that 
solutions of strong electrolytes do not fulfill the conditions of dilute 
solutions. Consequently, it is not possible to calculate from the electro- 
motive force of concentration cells the concentrations of the ions in 
solution ; for it may readily be shown, from electromotive force measure- 
ments, that the law of mass action does not apply to solutions of strong 
electrolytes and that, consequently, the laws of dilute solution do not 
apply. The ratios of the concentrations of the ions, therefore, cannot 
be calculated by means of the Nernst equation. 

It has been suggested that strong electrolytes are completely ionized 

even at fairly high concentrations. In that case the function J in 

s 

Equation 96 measures the change in the potential of the electrolyte due 
to interaction between the ions. Granting this assumption, the function 
Jg has a negative value at relatively low concentrations. With increas- 
ing concentration the value of J diminishes, passes through a minimum, 
and thereafter increases, passing through a value and becoming posi- 
tive at very high concentrations.^* 

A considerable number of measurements have been made on the 
electromotive force of concentration cells in which other electrolytes have 
been added to the solution of the electrolyte surrounding one electrode. 
Poma and Patroni^' have measured the electromotive force of copper 
electrodes in solutions of copper salts, to which various electrolytes 
with a common ion had been added. Poma^" measured the potential 
of the hydrogen electrode in acid solutions in the presence of other elec- 



OTHER PROPERTIED OF ELECTROLYTIC SOLUTIONS 303 

trolytes, both with and without a common ion. The results of Poma 
indicate a considerable change in the electromotive force due to the 
addition of another electrolyte. The effect varies with the concentra- 
tion and also with the nature of the added electrolyte. At the higher 
concentrations of added salt, at any rate, the effect is greatly dependent 
upon the nature of the added electrolyte, the electromotive force due to 
the addition of a given amount of electrolyte being the greater the 
greater the tendency of the salt to form hydrates. The sign of the 
electromotive force, moreover, was found to depend upon the nature of 
the added electrolyte. 

The results of Poma do not seem to be in good agreement with the 
results of other investigators who have investigated the electromotive 
force of similar cells. The potential of the hydrogen electrode in solu- 
tions of hydrochloric acid in the presence of varying amounts of alkali 
metal chlorides has been investigated by Chow," who found that, keep- 
ing the total ion concentration constant, the potential of the electrode 
in the mixture may be calculated according to Equation 95, the total 
concentration of hydrogen and of chlorine being employed for the con- 
centrations of the ions. According to this result, the function J remains 

constant in the mixture, provided the total concentration of the mixed 
electrolytes is maintained constant. Similar results have been obtained 
by Harned.^^ The results of Harned indicate that at low concentra- 
tions the function J,„ has the same value for the mixture as it has for 

o 

the pure electrolyte at the same total salt concentration. At higher con- 
centrations, according to Harned's measurements, the potential of the 
electrolyte depends upon the nature of the added electrolyte. It was 
also found that the potential of the hydrogen electrode in hydrochloric 
acid suffers nearly the same change due to the addition of equivalent 
amounts of potassium chloride and sodium bromide. 

As yet, experimental data in this direction are not sufficiently exten- 
sive to warrant generalizing the conclusions drawn from the investiga- 
tions referred to above. 

6. Thermal Properties of Electrolytic Solutions. It is only recently 
that the technique of thermal measurements has been refined to a point 
where data obtained with electrolytic solutions are sufficiently precise 
to make an inter-comparison of the various thermal properties of such 
solutions generally possible. Even now, accurate data are available for 
only a limited number of systems, as a result of which but few general 

"Cniow, J. Am. Chem. Soc. J,2, 497 (1920). 

"flarnea, /. Am. Chem. S<?c. J,2, 1808 (1930) ; i6i(?„ 37, 2460 (1915), 



304 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

conclusions may at the present time be reached relative to the manner 
in which the thermal quantities are dependent upon the various factors 
governing the condition of a solution. 

Water, itself, is ionized, and the energy of the ionization reaction 
corresponds very satisfactorily with the heats of neutralization of strong 
acids and bases. According to the Ionic Theory, the heats of neutraliza- 
tion of different strong acids and bases should be the same at low con- 
centrations, since the neutralization process under these conditions con- 
sists essentially in a combination of the hydrogen and hydroxyl ions to 
form water. The most reliable determination of the heats of neutraliza- 
tion was made by Wormann.^^ The mean value of the heat of neu- 
tralization for hydrochloric and nitric acids with sodium and potassium 
hydroxides at 18° was found to be approximately 13700 calories. The 
heat of ionization of water is related to the ionization constant of water 
by means of the equation: 

d log Z _ U 



(97) 



dr ~ RT' 



12' 



where U is the energy change accompanying the ionization of one mol 
of water. Noyes and his associates ^* have measured the ionization 
constant of water at a series of temperatures up to 218°. The heat of 
ionization derived from their results is in good agreement with the value 
found by Wormann for the heat of neutralization. Thus at 18° Noyes 
finds that the value 14055 is in agreement with his experimental values. 
Direct determinations of the heat of neutralization of strong acids and 
bases at higher temperatures do not appear to exist, so that a compari- 
son in these regions cannot be made. At higher temperatures the ioniza- 
tion constant of water passes through a maximum, as a consequence of 
which it follows that the heat of ionization changes sign. 

Equation 97 is likewise applicable to the ionization process of elec- 
trolytes in water. If the ionization values are known at different tem- 
peratures, the energy change accompanying the ionization process may 
be calculated, assuming that the energy change accompanying the process 
remains constant. The equation holds true even though the conditions 
for dilute systems are not fulfilled, provided the concentrations enter- 
ing in the equation represent the real concentrations of the molecular 
species in question. Thermal data of sufficient precision are not avail- 
able to make it possible to determine to what extent the results of con- 
ductance measurements at different temperatures are in agreement with 
thermal data. In a general way, however, the results appear to be in 
agreement. In the case of the weak acids and bases, the order of 

»" Wormann, Ann. D. Phys. IB, 775 (1905). 
"Carnegie Publications, No. 63 (1907). 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 305 

magnitude of the energy effects, as derived from conductance-temperature 
measurements, agrees with those derived from the heats of dilution of 
solutions of weak electrolytes. The ionization constants of acetic acid 
and ammonia, for example, have maxima in the neighborhood of ordi- 
nary temperatures, indicating that the energy change accompanying the 
ionization process is zero; correspondingly, the heats of dilution of 
solutions of these substances have small, although uncertain, values. In 
general, weak electrolytes have a greater heat of dilution than strong 
electrolytes and, correspondingly, their ionization changes more largely 
with temperature. 

The heats of dilution of strong electrolytes unquestionably have 
very small values. Correspondingly, the ionization of strong electrolytes 
at ordinary temperatures changes but little with temperature. The 
ionization of certain salts, such as magnesium sulphate, decreases 
markedly at higher temperatures ; and it is to be expected that solutions 
of these salts will exhibit an appreciable heat of dilution even at rela- 
tively low concentrations. Experimental determinations of these quan- 
tities, however, are lacking. In view of the uncertainty of the thermal 
data, it cannot be stated that the commonly accepted ionic theory leads 
to results which are in contradiction with the thermal properties of 
electrolytic solutions. 

Recently, careful determinations of the heats of dilution of a number 
of electrolytes have been made by a number of investigators. Accord- 
ing to Randall and Bisson,^^ the heat of dilution of sodium chloride from 
0.28 N to zero concentration amounts to only two calories. At higher 
concentrations the heat of dilution, although small, is quite marked. 
The heats of dilution of a number of salts, as well as of mixtures of 
salts, have been determined by Steam and Smith,'"' and Smith, Steam 
and Schneider.^^ The heats of dilution for sodium and potassium 
chlorides were found to be very nearly the same, although varying 
slightly at high concentrations. At low concentrations, the heat of dilu- 
tion, in all cases, approaches a value of zero, as might be expected. The 
heats of dilution are not in all cases of the same sign, since that of 
strontium chloride is opposite in sign from that of sodium and potassium 
chlorides. The heats of dilution for mixtures of two electrolytes in 
general differs markedly from the mean heat of dilution of the con- 
stituents. Stearn and Smith suggest that this result may be due to the 
fact that complex compounds, whose formation presumably would be 
accompanied by an energy change, are formed in mixtures of salts. For 
sodium and potassium chlorides the heat of dilution is negative, which 

■"Randall and Bisson, J. Am. Ghem. Soo. ^, 347 (1920). 
"Stearn and Smith, J. Am. Chem. Soc. *B. l? (1920). 
" Smith, Stearn and Schneider, itid., ^, 32 (1920). 



306 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

corresponds to an increase in the ionization of these electrolytes with the 
temperature. This is not in agreement with the observed results of 
conductance measurements. It is possible, however, that the energy- 
change measured on the dilution of a solution includes effects other than 
those due to change in the ionization of the electrolyte. Certainly, at 
the higher concentrations, it is to be expected that a change in the 
hydration of the ions, and possibly of the neutral molecules, takes place, 
and the energy change accompanying these processes may obscure the 
energy change due to the ionization process. 

It appears, thus, that a knowledge of the thermal properties of elec- 
trolytic solutions has a very direct bearing on our interpretation of the 
phenomena observed in electrolytic solutions. In order to analyze the 
more or less complex processes into their constituent effects, however, 
further experimental data are required. 

In this connection, it should also be noted that a number of investi- 
gators,'* from a study of the temperature coefficient of the electromotive 
force of concentration cells, have obtained values for the energy changes 
accompanying the transfer of electrolytes from solutions of one concen- 
tration to another. Harned has also determined the energy changes 
accompanying the transfer of hydrochloric acid from a solution con- 
taining a mixture of salt and acid to one containing acid alone. Hydro- 
chloric acid and chlorides were employed in these mixtures. 

In the following table are given values of the energy change accom- 
panying the transfer of one mol of electrolyte from the concentration 
given to a concentration of 0.1 N, according to Ellis and Harned. 

TABLE CXXVI. 

Energy Change, in Joules, Accompanying the Transfer of One 
Moii OF Electrolyte from a Concentration C to a Con- 
centration 0.1 N AT 25°. 



c 


KCl 


NaCl 


HCl 


0.1000 


000 


000 


000 


0.3000 


— 355 


— 300 


420 


0.5000 


— 650 


— 570 


820 


1.000 


— 1310 


— 1196 


1820 


1.500 


— 1900 


— 1780 


2770 


2.000 


— 2375 


— 2300 


3720 


2.500 


— 2810 


— 2690 


4740 


3.000 


— 3175 


— 3010 


5710 



As may be seen from the table, the energy changes accompanying the 
transfer of sodium and potassium chlorides differ but little. The sign of 

"BlUs, J. Am. Ohem. Soo. S8. 737 (1916) ; Harned, iUd., H. 1808 (1920). 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 307 

the energy change in the case of hydrochloric acid is opposite from that 
of sodium and potassium chlorides. 

Harned has also determined the energy changes accompanying the 
transfer of hydrochloric acid from solutions containing hydrochloric acid 
of concentration 0.1 N, together with an added salt having a common 
chloride ion at varying concentrations, C, to a solution of pure hydro- 
chloric acid at a concentration of 0.1 N. The results are given in the 
following table. 

TABLE CXXVII. 

Energy Change Accompanying the Transfer of Two Mols of HCl from Solutions 
OF 0.1 N HCl + CN MCI TO a Solution of 0.1 N HCl at 25°. 

KCl 

C 0.2018 0.5086 1.0346 2.134 3.309 

AH 6 37 149 1371 2807 

NaCl 

C 0.1003 0.2014 0.5061 0.9183 1.023 1.871 2.094 2.711 3.202 3.726 

A/f —44 142 273 569 755 2373 2381 3595 4647 5942 

LiCl 

C 0.8485 1.7267 2.636 3.574 4.556 

AH 1407 4128 6527 9200 11610 

It will be observed that the energy change is greatest for LiCl and 
least for KCl. Apparently, the energy change is greatest for those salts 
which exhibit the greatest tendency to form hydrates. These energy 
changes persist below 0.1 N. This is apparently also the case in solu- 
tions of the pure electrolytes.^" 

7. Change of the Transference Numbers at Low Concentrations. 
The transference numbers of an electrolyte are determined by the rela- 
tive speed of its ions. Any influence, therefore, which tends to alter the 
relative speed of the ions obviously tends to alter the transference num- 
bers of the electrolyte. The speed of the ions is a function of the vis- 
cosity of the solution and, for a given change of viscosity, the change in 
the speed of an ion depends upon the nature of the ion. This, for 
example, is evident from the effect of temperature on the ionic conduc- 
tances, where, as we have seen, the temperature effect is the smaller the 
greater the conductance of the ion. At higher concentrations, therefore, 
where the viscosity effect is appreciable, a change in the value of the 
transference numbers is not unexpected.^"" At low concentrations, how- 
ever, we should expect the transference numbers to be constant. 

This condition is apparently not fulfilled in solutions of strong acids 
and bases. For example, the anion transference number of hydrochloric 

"» Compare Ellis, loc. cit. 

'»« It has been found that the transference number of lithium chloride is not altered 
on the addition of raffinose (Millard, Thesis, Univ. of 111. (1914)). Reference to Table 



308 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

acid in water at 18° varies from 0.168 at 0.005 N to 0.165 at 0.1 N.*" 
In a sense, this does not appear to be a great change in the value of the 
transference number. Nevertheless, it is in excess of what might be 
expected from the viscosity effect in these solutions. Furthermore, the 
conductance of the chloride ion as calculated from the transference 
number and the degree of ionization does not correspond with the value 
of the conductance of the chloride ion at infinite dilution in solutions of 
potassium chloride. Assuming for the transference number of the 
chloride ion in hydrochloric acid the value 0.167 and for the ionization 
the value 0.972 and for the conductance the value 369.3 at 0.01 N and 
18°, we obtain, for the conductance of the chloride ion, the value 

Aqj = AjjqjX — = -nff^ = 62.68. At infinite dilution the con- 

ductance of the chloride ion has a value of 65.5. It appears, then, 
that up to a concentration of 0.01 N the conductance of the chloride ion 
has fallen from a value of 65.5 to a value of 62.68. This value is obvi- 
ously subject to a correction, since, in calculating the value of y by the 

ratio-r-, it has been tacitly assumed that the speed of the ions remains 
constant. 

Noyes ^^ called attention to this discrepancy which exists in the case 
of the strong acids. Lewis ^^ showed that the ionization of different 
chlorides as calculated from the conductance of the chloride ion at a 
given concentration is the same for all chlorides. Maclnnes *^ has inves- 
tigated the conductance of various ions at higher concentrations in some 
detail. The conductance of an ion at a given concentration is obtained 
by multiplying the conductance of the electrolyte by the transference 
number of the ion in question at that concentration. In the case of the 
chlorides, he obtained the following results: 

XLIII will show tbat the conductance of Iltliinm caesium nnd nr.(-ao«ii,m „i,i„„i.q < 
affected to almost the same extent on the addition of rSose w^dPHflf th^^^^^^^^ 
change due to raffinose affects the Li+, Cs+ and K+ iins to the same svi^;,!*^/*^'''*^'^^ 
same table, it is evident that the conductance of potasrium chloride Lflfthi,, ""?,? S^ 
la altered to very nearly the same extent, even on Uie addTtion of s„m? ,,in eWr''?'?'''*'? 
relatively low molecular weight. In methyl alcoliol however th„ S non-electrolyte of 
larger fir LiCl than for CsCl. In thrprestncc of ttN non electr^F^te'M" « '"'I'-'^edly 
viscosity on ion conductance depends upon the nature of the ?on Pn^i *^*^ '>?^",™<=t.,'j' 
lard (Joe. ««.) found that the transference number of the lUhium ion fnTth"?,^™^'^', ^^J' 
solutlon is decreased from 0.322 to 307 on the additiL ^? n^ Ion in lithium chloride 
per 1000 g. of water. The viscosity effect due to the e?eet?n1vte ffJi'if"! ™"'*''y %^'">^'>^ 
S? ll-ileTorcSrw-eVh?. '7n?o!ffe^W£H ^noS°el^^?^ofy?I 

l^n, ^the nature of the^articles^r^S^ tt^ ^^^ c<'h^anTe"='if ^u^mt^ Tot'.f.^^t 

» Noyes and Kato, J Am. Ohem. Soc. SO, 318 (1908) 

"Noyes and Sammet, J. Am. Chem Stni- pi. qA /iono\ . i.,., „- ,„_ 
/. phys Glwm.J,S 49 (1903) ; Noyes and Katofiftw ef 4^0 a90^')'^' ^^^ ^^^''^^ ' ^*^'^- 

.l}f^\^' ■'■ -i^vCT'*™- ^oc. 31,, 1631 (1912) " ' " (1908). 

"Maclnnes, J. Am. Chem. Soo. 1,1, 1086 (1919) ; mi., *J, 1217 (1921) 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 309 

TABLE CXXVIII. 

Conductance of the Chloride Ion at 18° as Derived prom the Con- 
ductance AND THE Transference Numbers of Different 
Electrolytes at 0.01 N and 18°. 

A ri Tci TciAriO- 

HCl 369.3 1.0005 0.167 61.67 

CsCl 125.07 0.9997 0.495 61.89 

KCl 122.37 0.9996 0.504 61.68 

NaCl 101.88 1.0009 0.604 61.55 

LiCl 91.97 1.0016 0.668 61.48 

Here Tqj is the transference number of the chloride ion and Tq^At)"-' 

is the conductance of the chloride ion corrected for viscosity. From an 
inspection of this table, it is evident that the conductance of the chloride 
ion, as derived from the transference numbers and conductances of dif- 
ferent chlorides, is the same. The ion conductances given in the last 
column have been corrected for the viscosity according to Equation 41, 
assuming for the exponent p the value 0.7. This viscosity correction is 
uncertain, but in view of the fact that the viscosity effect in all these 
solutions is scarcely in excess of 0.1 per cent it is evident that the vis- 
cosity correction can have only a minor influence. While the conduc- 
tance of the chloride ion in the different chlorides is very nearly the 
same, it does not appear to be identical. In lithium chloride, for ex- 
ample, the conductance is approximately 0.7 per cent lower than it is 
in caesium chloride, and from caesium chloride to lithium chloride the 
conductances vary in the order: caesium, potassium, sodium, lithium. 
If the differences were purely accidental, we should not expect any such 
regularity in the order of the conductance values. Maclnnes has also 
made a similar comparison at higher concentrations up to and including 
1.0 N. Throughout he obtains excellent agreement among the conduc- 
tance values of the chloride ion in different chlorides. It should be 
noted, however, that, at the higher concentrations, the viscosity effects 
are considerable, and the ion conductances in consequence are propor- 
tionately in doubt. 

Maclnnes is inclined to believe that it is generally true that at a 
given concentration the conductance due to a given ion is independent 
of the nature of other ions present in the solution. This generalization, 
however, does not appear to be wholly justified. For example, assuming 
the transference values given by Noyes and Falk, we obtain for the 
conductance of the nitrate ion at 0.2 N in solutions of KNO3, AgNOa 



310 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

and HNO3 the values 57.28, 55.60 and 56.40 respectively. There is, 
however, a considerable degree of uncertainty attached to these calcu- 
lations owing to uncertainties in the values of the transference numbers. 
The errors with which transference measurements are affected are rela- 
tively large and it is possible that consistent errors are present, in which 
case the probable error of the determination cannot be estimated from 
the consistency of a given series of measurements. In many respects, it 
would appear that transference measurements by the moving boundary 
method should be more nearly comparable than those by other methods. 
In Table CXXIX are given values of the ion conductance A 17-+ of the 

potassium ion and of for the same ion for different potassium 

Y 
salts at concentrations of 0.02 N and 0.1 N. The ionization and con- 
ductance values are taken from Noyes and Talk and the transference 
values from Dennison and Steele.^* The numbers in the next to the last 
column are the ion conductances, which should have the same value if 
the conductance of a given ion at a given concentration were independent 
of the nature of the other ion with which it is combined. In the last 

Aj7-+ 

column are given the values of which, if the transference num- 

y 
ber is independent of concentration and the ionization is measured by 

the ratio -r-, should correspond with the conductance of the potassium 
ion at infinite dilution. 



TABLE CXXIX. 

Values of A^+ and of foe Different Potassium Salts. 

At 0.02 N. 
Tc Y A^ A^. 



KCI 0.493 0.922 119.9 59.13 

KNO3 0.502 0.911 115.0 57 78 

KBr 0.482 0.921 121.7 58.68 

KCIO3 0.534 0.910 108.8 58.12 

KBr03 0.567 0.910 102.0 57.84 

^I 0.487 0.922 120.9 58.90 63 90 



A^ 

Y 
64.14 
63.44 
63.72 
63.88 
63.58 



Mean 58.41 Mean 63.78 
A.D. 0.50 A.D. 0.20 



"Dennison and Steele, PMl. Trans. A, SOS, 4G2 (19061. 



OTHER PROPERTIES OP ELECTROLYTIC SOLUTIONS 311 

TABLE CXXIX.— Continued 
At 0.1 N. 

^" yu A A^. -A 

KCl 130.0 0.861 111.97 55.10 64.04 

KNO3 126.3 0.829 104.71 52.60 63.50 

KBr 132.2 0.863 114.14 54.92 63.64 

KCIO3 119.6 0.829 99.14 53.17 64.14 

KBrOg 112.1 0.829 93.0 52.98 63.93 

KI 131.1 0.870 113.98 55.40 63.68 

Mean 54.03 Mean 63.82 
A.D. 1.11 A.D. 0.21 

It will be observed that at 0.02 N the value of A^+ varies from 57.78 

to 59.13 with a mean deviation of 0.50, while varies from 63.44 

Y 
to 64.14 with a mean deviation of 0.20. At a concentration of 0.1 N 
the value of A^+ varies from 52.60 to 55.40 with a mean deviation of 

1.11, while the value of varies from 63.50 to 64.14 with a mean 

deviation of 0.21. It is evident that the conductance of the potassium 

ion in different salts is not the same, while the ratio is substan- 

Y 
tially the same.^^ These results, therefore, do not bear out the conclu- 
sion that the conductance of an ion is independent of the other ion with 
which it is combined. Leaving aside for the moment the strong acids 
and bases, it appears that conductance and transference measurements 
agree with the assumption that the conductance of a given ion varies 
with the nature of its co-ion and that the difference in the conduction 
of a given ion is proportional to the ionization of its salt. The reason 
why the conductance of the chloride ion is foxmd the same for different 
electrolytes is due to the fact that the ionization of these electrolytes is 
the same at the same concentration. If corrected values of the con- 
ductance are employed, the ionization of sodium, potassium, and lithium 
.chlorides, as determined from conductance measurements, is substan- 
tially the same up to 1.0 N. Up to a concentration where the viscosity 
effects begin to become appreciable there is no certain evidence indicat- 
ing that the relative speeds of the ions undergo change. In the case of 

" This conclusion was reached by Dennison and Steele (Phil. Trans. A 205, 462 
(1906)). 



312 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the strong acids and bases, however, the experimental data indicate that 
the speed of one of the ions, at least, undergoes a marked change at 
concentrations below 10"^ N. The nature of the process to which this 
change is due remains uncertain. 

8. Reactions in Electrolytic Solutions. Electrolytic solutions, in 
water at least, are characterized by the speed with which they take place, 
as well as by their reversibility. This property of electrolytic solutions 
has been cited in support of the ionic theory; and, indeed, the reactions 
among electrolytes clearly indicate some common condition as a result 
of which they take place with great facility and, as a rule, with the 
accompaniment of a comparatively small energy change. It is only in 
a few other systems that reactions similarly take place with great speed, 
and many of these are irreversible. Reactions in fused salts and in the 
metals, however, resemble those in electrolytic solutions in many re- 
spects. There is little question but that reactions in fused salts are ionic 
in character. While available data are extremely meager in the case 
of the metals, there is evidence which indicates that here, too, reactions 
may be ionic. 

In a few instances, in water as well as in some other solvents, solu- 
tions of electrolytes do not reach equilibrium at once when an elec- 
trolyte is dissolved. In those cases which have been studied in detail, 
it has been shown that intermediate reactions occur which greatly influ- 
ence the properties of the solution; so, for example, certain of the metal- 
ammonia salts, when first dissolved in water, yield solutions which are 
very poor conductors of the current, but which, on standing, show a 
marked increase in conductance. Here, unquestionably, the gradual 
increase of the conductance is due to a reaction as a result of which the 
metal-ammonia complex is affected. The original complex is not capable 
of ionization, while the resulting product is ionized. These particular 
reactions are accounted for by Werner's theory. Aside from a few cases 
of this type, solutions of electrolytes reach a condition of equilibrium 
as soon as the process of solution is completed. 

It will be unnecessary, here, to discuss reactions in aqueous solutions 
since these are familiar to everyone who has studied the elements of 
chemistry. Since solutions in non-aqueous solvents are. ionized, we may 
expect that similar reactions take place in solutions in these solvents. 
The nature of the reactions will, of course, depend upon the nature of ■ 
the solvent as well as upon that of the dissolved electrolytes. 

The multiplicity of electrolytic reactions in aqueous solvents is in 
part due to the electrolytic properties of water itself. As we have seen, 
water is ionized to a slight extent into hydrogen and the hydroxyl ions! 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 313 

When one or more electrolytes are dissolved in water, the resulting reac- 
tion is influenced by the presence of these ions due to the solvent. We 
should expect similar reactions in the case of all solvents capable of 
ionization. This includes, in the first place, solvents containing hydro- 
gen, such as the liquid halogen acids, ammonia, hydrocyanic acid, formic 
acid, acetic acid, the alcohols, the amines, etc. In all these cases, it is 
to be anticipated that the solvent will furnish a positive hydrogen ion 
and a negative ion corresponding to the constitution of the solvent. The 
hydrogen or acid ion of substances dissolved in solvents which them- 
selves yield a hydrogen ion will exhibit acid properties. The negative 
ion, correspondingly, may be considered as a basic ion and salts of this 
ion will act as bases when dissolved in a solvent yielding the same ion. 
So, in the case of the alcohols, the acids exhibit acidic properties, while 
the alcoholates exhibit basic properties. Similarly, in ammonia, the 
ammonium salts exhibit acidic properties, while the basic amides exhibit 
basic properties. On the other hand, a base typical of water, such as 
tetramethylammonium hydroxide, would properly be classed as a salt 
when dissolved in ammonia. However, many of the characteristic prop- 
erties of acids and bases are not entirely dependent upon the presence 
of a positive or a negative ion in common with the solvent. For example, 
any salt of a strong base and a weak acid will exhibit properties charac- 
teristic of a base when in solution. Thus, tetramethylammonium hydrox- 
ide in ammonia exhibits basic properties, very similar to those of potas- 
sium amide, the reason for which lies in the fact that the resulting acid 
formed by the hydrolysis, or ammonolysis, of this salt in ammonia is a 
very weak acid water, which, as we know, is only very slightly ionized 
in liquid ammonia. Correspondingly, a cyanide dissolved in water 
exhibits basic properties for the reason that hydrocyanic acid is only 
slightly ionized in water. Strictly speaking, an acid has a positive ion 
and a base a negative ion in common with the solvent; nevertheless, 
salts of strong acids and very weak bases and salts of strong bases and 
very weak acids exhibit certain acidic and basic properties in solution. 
We have seen that the OH" ion is a characteristic basic ion only in 
aqueous solution and that in other solvents other ions function as basic 
ions. So, also, any positive ion common to a solvent will in that solvent 
exhibit many of the properties of an acid ion. For example, iron intro- 
duced into an aqueous solution of an acid yields a salt and hydrogen. 
Similarly, iron introduced into molten lead salt yields a corresponding 
salt of iron and metallic lead. Excepting for the fact that in the first 
case hydrogen is a gas and in the second case lead is a liquid metal, 
there is no essential distinction in the nature of the reaction in the two 



314 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

cases. The number of examples of this type might be greatly multiplied. 
Liquid ammonia is the only non-aqueous solvent in which electrolytic 
reactions have been extensively studied so that this discussion must be 
largely confined to solutions in this Solvent. The study of reactions in 
ammonia have led to a considerable extension of our notions respecting 
electrolytic reactions in general, and have greatly advanced our knowl- 
edge regarding the nature of various nitrogen compounds. Solutions in 
ammonia exhibit properties similar to those of solutions in water, be- 
cause of the similarity of constitution of the two solvents. In water we 
have the ionization reaction: 

H^O = H+ + OH- 

and in ammonia the corresponding reaction: 

NH3 = H" + NH/. 

The negative ions in ammonia and water differ, but exhibit many points 
of similarity. The positive ions in the two solvents are the same and 
exhibit a similar behavior. In ammonia solutions, however, the hydrogen 
ion appears to be identical with the ammonium ion, whereas in aqueous 
solution the hydrogen ion is in all likelihood a complex between hydro- 
gen and water, so that the two ions are not identical. The same is doubt- 
less true of most ions. In their essential behavior, however, the hydrogen 
ions in ammonia do not differ materially from the hydrogen ions in 
water. One of the characteristic properties of the hydrogen ions is its 
tendency to react with metals to form a salt and hydrogen. In water, 
for example, we have the reaction: 

Mg + 2HC1 = MgCl^ + H^. 

So, in ammonia we have the reaction: 

Mg + 2NH,C1 r= MgCl, + H2 + 2NH3. 

In this last reaction, the ammonia resulting from the reaction is identical 
with the solvent molecules and therefore may be omitted from the reac- 
tion equations. In aqueous solutions of the acids this is always done, 
for it is less evident that water is concerned in the reaction. In am- 
monia, the acids react with bases to form salts and water, corresponding 
to the reactions in aqueous solutions; thus: 

(CH3),N0H + HCl = (CH3),NC1 + H,0 in water, 
and (CH3),N0H + NH.Cl = (CH3),NC1 + NH3 + H,0 in ammonia. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 315 

In aqueous solutions, with a few exceptions, the acids are substances 
in which the hydrogen is joined to an electronegative group through an 
oxygen atom. For example, in the case of acetic acid we have 
CHgCOO'-H'^. Such acids are known as hydroxy-acids, or perhaps 
better aquo-acids, as Franklin has suggested. Similarly, in the case of 
ammonia, substances in which the hydrogen atoms are connected to an 
electronegative group through the intermediary of a nitrogen atom are 
acids. This is a class of substances commonly known as the acid amides 
or imides. Thus, we have, corresponding to acetic acid CH3COOH, 
acetamide CH3CONH2. Acetamide is therefore an acid related to am- 
monia as acetic acid is to water, and, according to Franklin, may be 
called an ammono-acid.*^ In view of the fact that nitrogen is tri-valent, 
the acid amides are dibasic acids in contrast with the corresponding aquo- 
acids which are mono-basic. As we have seen in an earlier chapter, the 
acid amides are soluble in ammonia and many of them are excellent con- 
ductors of the electric current. It has been shown that the acid amides 
and imides in ammonia possess characteristic acidic properties; that is, 
they react with the metals to form salts and hydrogen and with bases 
to form salts and ammonia. Thus we have: 

Mg + CH3CONH, = CH3C0NMg + H„ 

a reaction similar to that obtained with acetic acid in water. The acid 
amides likewise react with bases in ammonia to form salts and water; 
for example, 

CH3CONH, -I- (CH3),N0H = CH3C0NH(CH3),N + H,0. 

Acid amides in ammonia solution are weaker acids than the correspond- 
ing oxy-acids are in aqueous solutions, but this is to be expected, since 
the dielectric constant of ammonia is much lower than that of water and 
the ionization of all electrolytes is lower in ammonia than in water. 
However, as may be seen from the conductance values for the acid amides 
in ammonia solution as given in an earlier chapter, the ionization of 
certain of these acids in ammonia is as great as that of typical salts in 
this solvent. Relatively, therefore, the acid amides are as strong in 
ammonia as ordinary acids are in water. It is interesting to point out, 
in this connection, that, while the acid amides throughout exhibit acidic 
properties in ammonia solution, it is only in exceptional cases that they 
exhibit marked acidic properties in water. The reason for this is not 
well understood, but it seems probable that, when the acid amides are 

"Franklin, Am. Chem. J. i7, 285 (1912). See also numerous other articles by the 
same author in the Am. Cluim. J. and J. Am. Chem. 80c. 



316 , PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

dissolved in water, the basic properties of the nitrogen come into play 
and that compounds of a basic nature are formed similar to ammonium 
hydroxide, whicfli, however, are ionized only to an exceedingly small ex- 
tent, in view of the electronegative character of the rest of the molecule. 

As has already been pointed out, the basic amides, as for example 
potassium and sodium amides, are electrolytes in ammonia solution and, 
from their constitutional relation to ammonia, it is to be expected that 
solutions of these substances will exhibit basic properties in liquid am- 
monia. This is, indeed, the case. Potassium amide, dissolved in liquid 
ammonia, exhibits all the properties characteristic of bases. For ex- 
ample, it reacts with acids to form salts and ammonia; thus: 

CH3COOH + KNH, = CH3COOK + NH3. 

According to Franklin, bases of this type are called ammono-bases. 
Obviously, all basic amides belong to this class of substances. 

The ammono-bases react not only with aquo-acids but also with 
ammono-acids." Thus, an ammono-acid reacts with an ammono-base 
to form an acid ammono-salt and ammonia, according to the equation: 

CH3CONH, + KNH3 = CH3CONHK + NH3. 

It is interesting to note that the color reactions characteristic of indi- 
cators are likewise found reproduced in ammonia solutions.** Some 
indicators exhibit a remarkably sharp end point; as, for example, saf- 
franine. The nature of the indicator reactions have not, as yet, been 
studied in detail. 

In aqueous solutions, salts of weak acids aiid bases are hydrolyzed 
owing to interaction between the ions of the solvent with those of the 
dissolved salt. So, also, in ammonia solutions, the salts of very weak 
acids and bases are ammonolyzed; that is, the salt reacts with the sol- 
vent to form an acid and a base. Unfortunately, the extent to which 
ammonia is ionized into H* and NH^- ions is not known. In all likeli- 
hood, however, the concentration of these ions is extremely low, since 
the alkali metals are soluble in liquid ammonia and remain in solution 
for extended periods of time with only a slight reaction, according to 
the equation: 

Nil3 + Na = NaNH, + JH,. 

If the concentration of the hydrogen ions were considerable, this reaction 
should take place with great rapidity just as the corresponding reaction 
takes place m water. That hydrolysis (or ammonolysis) actually takes 

"Franklin and Stafford, Am.. Chem J ',< U<i liano\ 
"Franklin and Kraus, Am. ChcmliiJ^T (WOO) .' 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 317 

place, however, has been definitely shown. As a consequence of the 
very low concentration of the H+ and NHa" ions in ammonia, it is only 
in the case of salts of extremely weak acids or bases that hydrolysis has 
been observed. For example, when mercuric chloride is dissolved in 
ammonia the following reaction occurs: 

HgCl, + NH,- + NH3 = HgNH.Cl + NH.Cl. 

In this case, the compound HgNHjCl is insoluble and is precipitated. 
Obviously, this precipitation proceeds until the concentration of NH^Cl 
is sufficiently great to bring the reaction to equilibrium. The addition 
of an ammonium salt, which raises the concentration of the NH/ (hydro- 
gen) ions, reverses the reaction, causing the precipitate to go into solu- 
tion; while, on the other hand, the addition of an ammono-base, KNHj, 
for example, results in an increased precipitation. In most instances, 
however, salts dissolve in ammonia without appreciable ammonolysis. 
This is indicated by the fact that in many cases the resulting base or 
basic salt is practically insoluble and even a small degree of ammonolysis 
would result in the formation of a precipitate. Since in the great ma- 
jority of cases the salts yield clear solutions, it is obvious that am- 
monolysis does not occur to an appreciable extent. 

A considerable number of reactions have been studied in solvents of 
very low dielectric constants *^ such as benzene, toluene, etc. Reactions 
in these solvents often take place readily and even instantaneously. As 
a rule the salts dissolved are heavy metal salts of the higher organic 
acids such as the oleates, stearates, etc. It has been claimed that solu- 
tions of these salts are non-conductors, but the work of Cady and 
Lichtenwalter indicates that, while the order of conductance of solutions 
of salts of organic acids in benzene is low compared with that of ordi- 
nary solutions of electrolytes, nevertheless, benzene solutions conduct 
iar more readily than does the pure solvent. In the case of a metathetic 
reaction with hydrochloric acid, the conductance was found to rise largely 
before precipitation, due, presumably, to the relatively greater con- 
ductance of the more concentrated supersaturated solution. That solu- 
tions of salts in such solvents as benzene are sufficiently ionized to exert 
a marked influence on the conductance is not to be doubted. 

Metathetic reactions take place readily in solutions in solvents of 
low dielectric constants such as benzene, but, apparently, these reactions 
are not always instantaneous.^" This result may in part be due to the 

«Kahlenberg, J. Phvs. Ohem. 6, 1 (1902) ; Sammis, ibid., 10, 593 (1906) ; Gates, 
ibid 15 97 (1911) ; Cady and Lichtenwalter, J. Am. Chem. Soc. S5, 1434 (191.'!) ; Cady 
and 'Balciwin, ibU., iS, 646 (1921). 

»» Cady and Lichtenwalter, loc. cit. 



318 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

formation of supersaturated solutions. Reactions between silver per- 
chlorate and hydrochloric acid, mercuric chloride and trimethyltin 
chloride take place instantaneously in benzene.^^ Small amounts of 
water greatly influence the conductance of solutions of this type. 

While these results are in good agreement with the ionic hypothesis, 
it cannot be said that reactions cannot take place between the un- 
ionized molecules. For example, methyl iodide precipitates silver iodide 
in solutions of silver perchlorate in benzene. If reactions of this type 
are ionic, we must modify, somewhat, our notions relative to the nature 
of organic compounds. Yet not a few facts are in excellent agreement 
with such a view. 

Reactions of the electrolytic type, in which one metal is substituted 
by another more electropositive metal, have also been studied in sol- 
vents of low dielectric constants. ^^ Such reactions often take place 
readily. It appears not unlikely that they are in fact electrolytic. The 
properties of solutions of substances of the electrolytic type in solvents 
of low dielectric constant have received all too little attention. The 
data so far are too fragmentary to warrant drawing conclusions of a 
general nature, but it is not to be doubted that the study of such systems 
will lead to important results. Electrolytic phenomena are not confined 
to solvents of high dielectric constant. Evidence is constantly accumu- 
lating which supports the view that all fluid media possess, in some 
degree, the power of forming electrolytic solutions under suitable con- 
ditions. 

9. Factors Influencing Ionization, a. The Ionizing Power of Sol- 
vents in Relation to Their Constitution. Since, as we have seen, the 
ionizing power of a solvent is largely determined by its dielectric con- 
stant, it follows that, in seeking to determine possible relations between 
the constitution of a substance and its ionizing power, we should seek 
for relations between the dielectric constant and the constitution of the 
substance in question. Water, hydrocyanic acid and formamide have 
the highest dielectric constants of substances so far investigated. 

The nature of the relation between the dielectric constant and the 
constitution of liquid media is not clear. There is, however, an obvious 
relation between the dielectric constant of the hydrogen derivatives of 
the elements and their position in the periodic system. The hydrogen 
derivatives of the first members of the various groups invariably exhibit 
a dielectric constant much greater than that of the following members. 
Similarly, the dielectric constant of the hydrogen derivatives of elements 

"GatesrJoT^t'' ^^^'"'^' "^''"'' "°"^ ^^^^"^ '° ^^^ Author's Laboratory. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 319 

in a given series increases with the order of the group. Thus, water 
has a dielectric constant of approximately 80 and is an excellent ioniz- 
ing agent, while hydrogen sulphide has a dielectric constant of 10 and 
is a relatively poor ionizing agent. Ammonia at its boiling point has 
a dielectric constant of 22 and is a moderately good ionizing agent. In 
the seventh group, hydriodic acid has a dielectric constant of 2.9, hydro- 
bromic acid of 6.3, and hydrochloric acid of 9.5. As we approach the 
derivatives of the upper members of this group, their dielectric constant 
and their ionizing power increase. The dielectric constant of hydrogen 
fluoride is not known but it is known to be an excellent ionizing agent. 
Moissan, for example, prepared fluorine by the electrolysis of fluorides 
in liquid hydrogen fluoride. It seems not improbable that the dielectric 
constant of hydrofluoric acid is greater than that of water. At any rate, 
in passing from ammonia to water, the dielectric constant increases from 
22 to 80, and it is, therefore, not improbable that the dielectric constant 
of hydrogen fluoride is higher than that of water. The dielectric con- 
stant of many organic and inorganic substances containing oxygen, nitro- 
gen, chlorine and sulphur is relatively high. Such substances in the 
liquid state possess the power of dissolving salts and of forming conduct- 
ing solutions with them. It is unnecessary to give here a detailed list of 
these substances. 

With increasing temperature, the dielectric constant of all substances 
decreases. The dielectric constants of a number of substances have been 
measured through the critical point.^^ These include sulphur dioxide, 
ether, ethylchloride, and hydrogen sulphide. For these substances the 
dielectric constant just beyond the critical point is 2.1, 1.52, 4.68 and 2.7 
respectively. A striking result, here, is the relatively high value of the 
dielectric constant of ethylchloride at the critical point relative to its 
value at lower temperatures. Thus at 59° its value is 6.29, which de- 
creases to the value given above at 186°. Evidently the variation of 
the dielectric constant with the temperature depends largely upon the 
nature of the solvent. Corresponding to the low value of the dielectric 
constant of sulphur dioxide, the conductance of solutions of electrolytes in 
this solvent falls to very low values. The same is true of ammonia solu- 
tions, although in this solvent the conductance above the critical point 
has a readily measurable value. The conductance of typical salts in 
ethylchloride has not been measured, but that of mercuric chloride 
solutions, whose ionization is usually relatively low, is greater than 
that of solutions of typical electrolytes in sulphur dioxide under 
corresponding conditions. Judging by the conductance of solutions 

MEversheim, Ann. d. Phys. 8, 539 (1902) ; iUd.j IS, 492 (1904). 



320 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

in the critical regions, solvents which have a dielectric constant greater 
than 26 at ordinary temperatures have fairly high dielectric con- 
stants in the critical region; and, probably, the higher the dielectric 
constant of solvents of this type, the greater the dielectric constant in 
the critical region. In all likelihood, the dielectric constant of water in 
the critical region is fairly high. Unfortunately, there are very few data 
available on the relation between the dielectric constant and the variables 
which determine the condition of the solvent. 

Among solvents of high dielectric constant, only solutions in water 
have been measured with any considerable degree of precision. The 
conductance of solutions in hydrocyanic acid indicates that the behavior 
of solutions of electrolytes in this solvent is similar to that in aqueous 
solutions, but available data are not sufficiently accurate to make it 
possible to determine the precise form of the conductance curve. Fur- 
ther data on the properties of solutions in solvents of high dielectric con- 
stant are much needed. 

b. The Relation between the Ionization Process and the Constitution 
of the Electrolyte. While the ionization of an electrolyte is, in the first 
place, largely dependent on the dielectric constant of the solvent medium, 
the strongest typical electrolytes are probably ionized in all solvents, 
provided they are sufficiently soluble, but in solvents of very low dielec- 
tric constant ionization is appreciable only at high concentrations. The 
typical inorganic salts are not, as a rule, sufiBciently soluble in solvents 
of low dielectric constant to yield solutions which conduct the current 
readily. However, salts of various organic bases, such as the substituted 
ammonium salts " are soluble in solvents of low dielectric constant and 
conduct the current. 

The dielectric constant is only one of the factors governing the ion- 
ization process. For ionization is largely dependent upon the nature of 
the second component. For certain substances, which we ordinarily class 
as the typical salts, the dielectric constant of the solvent medium is 
largely determinative of the ionization, but even here we find that in 
non-aqueous solvents the ionization may vary greatly for salts whose 
ionization values are practically identical in water. This is true of solu- 
tions in ammonia and still more so of solutions in acetone. In these 
solvents, the characteristic properties of the electrolyte persist even down 
to the lowest concentrations for which measurements exist and these con- 
centrations are much lower than those in aqueous solutions. No theory 
of electrolytic solutions can be looked upon as adequate which does not 
Tender an account of this very common property of these solutions. 

"WaWen, Bull. Acad. Imp. dea Sci., p. y07, No. 16 (1013), VI series. 



OTHER PROPERTIES OF ELECTROLYTIC SOLUTIONS 321 

In general, compounds between strongly electronegative and strongly 
electropositive constituents are electrolytes both in solution and in the 
fused state. This includes not only salts of strong acids and bases but 
also salts of weaker acids and bases. Thus, the ammonium salts are ex- 
cellent conductors both in solution and in the fused state. The same is 
true of salts of organic bases. Here, however, we find a few marked excep- 
tions. Thus, the trimethylin halides, (CH3)3SnX are normally ionized 
in aqueous solution, but are ionized much less than other typical salts 
in alcohol and still less in acetone. In nitrobenzene and benzonitrile 
these salts are not ionized at all, although these solvents have dielectric 
constants higher than that of alcohol. Finally, these salts are not appre- 
ciably ionized in the liquid state.== It is evident that we have here an 
extreme case of individuality in an electrolytic substance. 

In many cases, the electrolytic properties of a solution are due to 
interaction between the solvent and the solute whereby an electrolyte 
is produced. Thus, the acids are electrolytes in solution but in the pure 
state they exhibit a very low conductance. Indeed, the acids are electro- 
lytes only in what may be termed basic solvents ; that is, solvents capable 
of forming salts or salt-like substances on addition to an acid. Ammonia 
and ammonium salts are typical examples of a solvent and a salt of this 
type. Solutions of the acids in water and the alcohols probably depend 
for their electrolytic properties on the formation of similar complexes 
between the acid and the solvent.^^ When acids are dissolved in non- 
basic solvents, such as sulphur dioxide or nitrobenzol, the resulting solu- 
tions exhibit a very low conductance, provided the solvent is quite dry. 
Doubtless, similar considerations hold for solutions of acidic substances, 
such as the acid amides in ammonia.^' So, also, solutions of many 
organic oxygen and nitrogen compounds in the liquid halogen acids owe 
their electrolytic properties to the formation of a more or less stable 
complex between the dissolved substance and the acid solvent. The 
inorganic bases, while intimately related to the acids from the standpoint 
of their constitution in aqueous solution, are otherwise to be classed as 
salts. The properties which they exhibit are throughout characteristic 
of salts. 

In general, compounds, in which distinctly electropositive and electro- 
negative constituents are not present, are not electrolytes; or, at any 
rate, in a fused state they are relatively poor conductors of the electric 

|» Observations by Mr. C. C. CaUis in the Author's Laboratory. 

== Kendall and Gross, J. Am. Ohem. Soc. p, 1426 (1921), have investigated the con- 
ductance of mixtures of acids with esters, ketones and other acids and have found unmis- 
takable signs of the formation of compounds. 

" The acid amides do not conduct in water probably owing to the fact that these 
substances act as very weak bases in water, whose acidic properties are much greater 
than those of ammonia. 



322 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

current and in solution their conductance is low. Nevertheless, solutions 
of non-polar substances may exhibit marked electrolytic properties. So, 
for example, solutions of iodine bromide, iodine trichloride, iodine, phos- 
phorus trichloride, phosphorus pentabromide, etc., conduct the current to 
a measurable extent in sulphur dioxide, arsenic trichloride, sulfuryl chlo- 
ride, nitrobenzene,^* etc. So, also, for example, solutions of iodine in 
bromine conduct the current. Walden has suggested that in these solu- 
tions one electronegative atom functions as anion and another as cation. 
For example, he assumes that a reaction of the type: 

I2 = I^ + I-, 

takes place when iodine is dissolved in sulphur dioxide. The investiga- 
tions of Bruner and Galecki ^^ and Bruner and Bekier '"' have shown that, 
in sulphur dioxide and nitrobenzol, the halogens and their compounds 
are not constituents of the positive ions. At any rate, on electrolyzing 
such solutions, the negative element may be concentrated at the anode. 
The nature of the cation in these solutions is uncertain, but there appears 
to be little doubt that the electronegative constituent is associated with 
the anion. Apparently, the electrolytic properties of these solutions are 
due to the formation of a complex between the strongly electronegative 
element or compound and the solvent, in which, presumably, the solvent 
molecule, in part at least, functions as cation. 

So far as the electrolytic properties of their compounds are concerned, 
strongly electronegative elements or groups of elements may not function 
as cations, although it is possible that in certain cases they may be asso- 
ciated with the cation in the form of a complex ion, as is the case, for 
example, with iodine in the intermediate ion of cadmium iodide in 
aqueous solution. On the other hand, as we have already seen, metals, 
which normally are electropositively charged in their compounds with 
more electronegative elements, may, under certain conditions, function as 
anions. For example, sodium and lead in ammonia react to form a solu- 
tion in which the two elements are present in the ratio of 2.25 atoms of 
lead to one atom of sodium, when metallic lead is present in excess." 
On electrolysis of these solutions, lead is precipitated on the anode. The 
properties of these complex anions have already been discussed. 

» Walden, Ztschr. f. phus. Chem. iS, 385 (1903). 

M§''"°^'^ and GalecM, Ztschr. f. phys. Ohem. 8i, 513 (1913). 

"Bruner and Bekier, iBW., 84, 570 (1913) 

"Kraus, J. Am. Chem. Soc. 29, 1557 (1907) ; Smyth, iUd., 39, 1299 (1917). 



Chapter XII. 
Theories Relating to Electrolytic Solutions. 

1. Outline of the Problem Presented by Solutions of Electrolytes. 
The problem of electrolytic conduction presents a twofold aspect depend- 
ing upon the point of view from which it is approached. On the one 
hand, we are concerned with certain well defined equilibria, the laws 
governing which it is attempted to discover; on the other, we are con- 
cerned with the mechanism of the process whereby the conduction of the 
electric current is effected. In the first case the principles governing 
equilibria in mixtures are applied, supported by various auxiliary assump- 
tions which are necessary if an explicit solution of the problem is to be 
reached. These assumptions usually involve the equation of state of 
the system, the precise form of which is not known. A general solution, 
therefore, cannot be reached by this method. In order to disclose the 
mechanism of the conduction process, a knowledge of the forces acting 
between the conducting particles and their surroundings is required. 
Since the laws governing these forces are not known, a solution is not 
possible by this method. Furthermore, if a force function is assumed, 
a solution can be reached only by the application of statistical methods 
and these methods have not been developed to a point where their appli- 
cation to electrolytic systems can be made with any degree of certainty. 
In either case, therefore, a point is soon reached where the results ob- 
tained are little more than conjectures. The probable correctness of the 
results obtained may be checked by comparison with experiment. In 
practice it is often found that, while the results of one method agree 
fairly well among themselves, they disagree with those obtained by the 
alternative method. That the two methods must lead to results which 
are in mutual agreement is not to be doubted. Lack of agreement indi- 
cates that various assumptions made are not permissible. 

It may be expected that a solution of the problem will first be reached 
for mixtures where the concentration of the electrolytic component is so 
low that various effects, due to the interaction of the ions and other mo- 
lecular species present, become negligible. Here, however, the difliculty 
arises that experimental data become very uncertain. Nevertheless, ap- 

323 



324 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

preciable progress has been made in this direction. In dilute solutions of . 
weak electrolytes, the ionic theory has met with marked success and, 
while it may be expected that here, too, the theory will have to be 
materially modified when a final solution of the problem has been reached, 
the mutual consistency of the results obtained indicates that a consider- 
able measure of truth underlies the ionic theory as formulated. This 
important fact should not be lost sight of in developing a more general 
theory of electrolytic solutions. 

The inapplicability of the law of mass action in its simple form to 
relatively dilute solutions of strong electrolytes has led to many contro- 
versies relative to the nature of these solutions. On the one hand, it has 
been suggested that such solutions are completely ionized at all concen- 
trations; 1 and, on the other, that they are not ionized at all.^ Still other 
theories attempt to relate these solutions with colloidal systems.^ The 
proposed theories may be grouped into three classes: (1) theories which 
are derived by combining with thermodynamic principles auxiliary 
assumptions, which, in part at least, are of an empirical nature; (2) 
theories in which the interionic forces due to the charges are taken into 
account; and (3) theories of a miscellaneous nature which as a rule are 
of a qualitative character. 

2. Electrolytic Solutions from the Thermodynamic Point of View. 
a. Scope of the Thermodynamic Method. If equilibria exist in solu- 
tions of electrolytes, as we have reason to believe, then such solutions 
must be subject to the thermodynamic principles governing equilibria. 
That equilibria, in fact, exist in electrolytic systems is not to be doubted, 
since in no other class of systems do reactions proceed so rapidly to a 
definite condition. In most instances, it is not possible to measure the 
speed with which reaction takes place in these solutions. The first 
assumption which arises in the detailed application of the principles of 
thermodynamics to equilibria in solutions of electrolytes is that of the 
■precise nature of the reaction involved. It is obvious that, before equi- 
libria of the electrolytic type can be treated comprehensively, the nature 
of the reactions involved must be definitely established. All considera- 
tions in which these reactions are involved are necessarily subject to 
uncertainty, since it has not been found possible to establish, definitely, 
whether or not un-ionized molecules, as well as ions, exist in electrolytic 
solutions. The nature of the reaction being assumed, the thermodynamic 
treatment of electrolytic solutions is comparatively simple, so far as the 
thermodynamic considerations themselves are concerned. When, how- 

' Ghosh, Trans. Cliem. Soe. 113, 449 (1918) 

"Snethlage, Ztschr. /, phys. Chem. 90, 1 (1915) 

» GeorgieviCB, Ztschr. }. phys. Chem. 90, 341 (19X5), 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 325 

ever, the concentrations of the various constituents present in the solu- 
tion are such that the laws of ideal systems are no longer applicable 
within the limits of experimental error, a general solution of the problem 
is, at the present time, not possible. In other words, the general solution 
of the problem involves a knowledge of the equation of state of the 
system. According to the equilibrium principle of Gibbs, a system will 
be in stable equilibrium when the entropy is a maximum. For many 
purposes it is more convenient to introduce derived functions such as the 
Gibbsian functions ■\\> and t, in place of the entropy. For a mixture of any 
number of components in a system, not subject to reaction, the free energy 
is given by the equation: 



(98) 

-{-xlogx 



pdv -\- RT [{1-x-y-z-- ■) log (1-x-y-z---) 

V 

-y\ogy -\-z\ogz + ---] -\- F{xyz . .T), 



where x, y, z, etc., represent the amounts of the various constituents pres- 
ent per gram mol of the mixture. The term F (xyz . . T) is, in general, a 
determinable function of temperature and a linear function of xyz . . . 
The term f pdv is a function of the concentrations xyz . . , and represents 

JV 

the work done in bringing the system from a condition in which the laws 
of an ideal system are obeyed to the condition in which the system obeys 
any given equation of state.* It is obvious that the condition for equi- 
librium, di|) = 0, may at once be applied if the equation of state is 
known, while, if the equation of state is not known, the problem is neces- 
sarily insoluble, since it is not possible to evaluate the integral in ques- 
tion. When reaction takes place between various constituents present in 
the mixture, the condition for equilibrium leads to the equation: 

(99) 2M = 0, 
where 

(100) Af = in\i. 

Here m is the molecular weight of the constituent and \i is the thermo- 
dynamic potential defined according to Gibbs.'' The molecular potential 
M, of a constituent, is given by an equation of the form: 

(101) M = RT\ogx + F{vT xyz..) 

where F{vT xyz- .) is a function of the composition of the system, as 
well as of volume and temperature, except when the equation of state of 

nrnn <ler Waals-Kohnstamm, "Lehrbuch der Thermodynamik," Vol. 2 (1912). 
»Sbbs, Scientific Papers, Vol. 1, pp. 92 et seg. (1912). 



326 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the system fulfills the condition pv = RT, in which case the only manner 
in which the concentration is involved in the expression for the thermo- 
dynamic potential is in the logarithmic term of the above equation. In 
order to evaluate the term F(vT xyz. .) it is necessary to know the equa- 
tion of state of the system, since the value of M as given by the equation: 

(102) ^ = ^-^(l!-Xr-KllXr--- 

obviously involves the term [ pdv, which cannot be evaluated without 

a knowledge of the equation of state. The equations of state for mix- 
tures of ordinary liquids are comparatively complex, and a general solu- 
tion of the problem has not been effected, even for liquids of simple type; 
while, in the case of mixtures of substances whose equations of state are 
comparatively complex, even an approximate solution has been little more 
than attempted. This subject has been treated in detail by van der 
Waals." 

b. John's Theory of Electrolytic Solutions. Nernst' and Jahn^ 
attempted to solve the problem of solutions of strong electrolytes by 
introducing various correction terms. Since the true equation of state 
for mixtures containing electrolytes is not known, even approximately, 
it is obvious that these theories necessarily involve assumptions of an 
arbitrary nature. These assumptions must contain within them the 
equivalent of an equation of state. In how far these assumptions are 
allowable may be ascertained by comparing the consequences of these 
theories with the experimental facts. Jahn set up the conditions for 
equilibrium, employing as a criterion for equilibrium, the variation of 
Planck's function: 

"f — r 

It is on the whole immaterial what function is employed as criterion for 
equilibrium, provided, always, that it fulfills the conditions of a charac- 
teristic function.^ These functions involve the energy of the system and, 
in order that the condition for equilibrium may be solved, it is necessary 
to have an expression for the energy of the system in terms of its com- 
position. In the case of ideal systems, Dalton's law may be assumed to 
hold, in which case the energy of a mixture of substances is equal to the 
sum of the energies of its constituents. Jahn assumed an equation for 

" van der Waals-Kohnstamm, loc. cit. 
' Nernst, Ztschr. f. phys. Ohem. S8. 487 (1901). 
'Jahn, Ztschr. f. pli/ya. Ohem. J,l, 257 (1902). 
•Glbbs, Scientiflc Papers 1, pp. 85 et aeq. (1906). 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 327 

the energy containing cross terms due to forces acting between the dif- 
ferent molecular species present in the mixture. This assumption, which 
is necessary for a solution of the problem by this method, is obviously 
an arbitrary one. Proceeding in this way Jahn obtains, for a system of 
electrolytes in equilibrium, the equation: 

(103) log -J- =(.a+ Py) C + log Ko, 

where a and p are constants. The constancy of the functions a and p 
however, depends upon the original assumption made with regard to the 
manner in which the energy of the system is dependent upon its composi- 
tion, and, if a different assumption had been made, it would have led to a 
corresponding variation in the resulting equation. Methods of this kind 
are correct enough thermodynamically, but, in order that they may lead 
to results which may be tested experimentally, an assumption must be 
made, and this assumption is, in general, arbitrary in its nature. In this 
sense, therefore, the results of these methods are to be looked upon as 
being purely empirical in character, unless evidence of an a priori nature 
can be adduced in favor of the assumptions made. In all cases, the cor- 
rectness of the assumptions may be tested by comparing the resulting 
equations with the experimental values. Taking the equation of Jahn, 
it is easy to make a comparison with experiment. 

This equation obviously involves four constants ; namely, a, p and Ko, 
together with Ao, the limiting value of the equivalent conductance. The 
equation is a fairly complex one and it is not easy to extrapolate for the 
value of Ao on the basis of this equation, but it may safely be assumed 
that, in the case of potassium chloride, the conductance of whose solutions 
has been measured to 2 X 10"^ normal, the true value of Ao does not 
differ materially from that ordinarily assumed. At higher concentra- 
tions, at any rate, a slight error in the value of Ao will cause a relatively 
small change in the distribution of the points. Assuming the value of 
Ao, and calculating the values of the function K' at three concentrations, 
it is possible to evaluate the constants a, p and Ko. The values of a and 
P being known, the equation may be tested by plotting values of log K 
against those of (a + Py) C. This plot should yield a linear relation, 
but in fact, leads to results inconsistent with the experimental values. 
The value of K' has a maximum in the neighborhood of 0.05 normal, 
after which it decreases rapidly. The equation as calculated for potas- 
sium chloride at 18° is as follows: 

log K' = 2.5935 + (592.8 — 498.7y)C. 



328 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

While Jahn's equation has not been tested in the case of non-aqueous 
solutions, it is easy to see that it cannot hold generally. For example, 
for m = 1 in Equation 11, the function K' varies practically as a linear 
function of the ion concentration. Such an equation will not reduce to 
the form of that of Jahn. 

That Jahn's equation should not hold is in no wise surprising, since 
the assumptions underlying it are of an arbitrary nature. It is improb- 
able that the free energy of electrolytic solutions may be determined as a 
function of concentration without the aid of an equation of state. In 
other words, the chance of finding the correct equation by mere accident 
would appear to be vanishingly small. The method of Nernst does not 
differ materially from that of Jahn and leads to a similar result. 

c. Comparison of the Thermodynamic Properties of Electrolytes. 
Inconsistencies in the Older Ionic Theory. While the application of 
thermodynamic principles yields no information relative to the mecha- 
nism involved in electrolytic solutions, these principles when combined 
with other hypotheses lead to consequences which admit of verification. 

The bearing of thermodynamics on the theory of electrolytic solutions 
was long neglected and has often been misinterpreted. So, for example, 
the correspondence between the ionization values as derived from con- 
ductance and from osmotic measurements was looked upon as lending 
support to the older ionic theory. As Nernst " pointed out, this apparent 
confirmation of the ionic theory constitutes, in fact, one of the chief 
obstacles in the path of its acceptance. 

Insofar as electrolytic solutions constitute systems in which equilibria 
prevail, thermodynamic principles are applicable. It is evident, how- 
ever, that the laws of dilute solutions are not applicable to these systems 
at ordinary concentrations. Aside from a few very general relations 
the application of thermodynamic principles alone can furnish us very 
little information relative to the nature of these solutions. The general 
problem is to express the potentials of the various constituents in terms 
of the independent variables of the system; that is, of the concentrations 
of the various substances present. Since statistical and other methods 
have not been developed to a point where they enable us to determine the 
equation of state of these systems, the problem at the present time can 
be attacked only by experimental methods. Fortunately, the potentials 
of electrolytes in solution may be determined readily and with a rela- 
tively high degree of precision. The values of the potentials as thus 
determmed may be treated by graphical or other empirical methods- and 
while the theoretical relation between the potentials and the concentra- 

'» Nernst, ZUohr. f. phys. Chem. 38, 493 (1901) ; Jahn, iUd., S8, 125 (1901). 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 329 

tions of the constituent electrolytes remains undisclosed, the form of the 
function may be determined. At the same time, the values of the poten- 
tials of different electrolytes may be compared and relationships brought 
to light which are of practical importance, even though their theoretical 
significance may not be apparent. Our knowledge of electrolytes from 
this point of view is restricted to aqueous solutions. In view of the fact 
that many properties of electrolytic solutions are greatly modified in 
solvents of lower dielectric constant, and since the similarity in the be- 
havior of dilute aqueous solutions of different electrolytes is not often 
found in other solvents, any generalization of the results obtained in 
aqueous solutions must be made with caution. 

The Thermodynamic Method. The significance of the results ob- 
tained from an examination of the thermodynamic properties of electro- 
lytic solutions will be better understood if treated without reference to 
detailed methods. Let us assume that we have a solution in which the 
following reaction takes place: 

n^A^ + n^A^ + ■ • ■ = n/^/ -f n/A/ + ■ • • 

The condition for equilibrium in such a solution is: 

(104) ^nM = lln'M'. 

The potential sum for the constituents on either side of the reaction equa- 
tion may be expressed by a function of the form: 

(105) 2nM = F(C„C„. . .C,',C/,. ..), 

where C-^fi.^,. ■ .C^ ,C^' ,. . . are independent variables. If any of these 
variables are not independent, a relation will evidently exist among them 
by means of which they may be eliminated. So long as we are dealing 
with a solution of a single electrolyte, the potential may obviously be 
expressed as a function of the concentrations of the ions and the un-ion- 
ized fraction; that is, we have: 

(106) ^nM = F{C\C-,C^). 

Since a relation exists between the concentrations C\ C" and C^^, it is 
obvious that one of these variables is not independent. Since, in general, 
it is not possible to determine the concentration of the ions and of the 
un-ionized fraction in a solution of an electrolyte, the total concentration 
of the salt may equally well be employed for practical purposes, in which 

(107) 2nM = /^{Cp. 



330 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

If the value of the potential sum 2nM may be experimentally determined 
at different concentrations, the form of the function F{Cg) is empirically 

known. If the experimental values of 2nM are correct, then the values 
of i*'(C ), as determined by different methods, must necessarily be in 

agreement. This result has been verified by Lewis and Randall,^"* as 
we shall see below. When mixtures of electrolytes are employed, the 
expression for the potential obviously becomes a function of a greater 
number of variables. In the case of a salt in the presence of another salt 
with a common ion, the potential becomes a function of two variables; 
and in that of a salt without a common ion, of three variables. We 
should not expect, therefore, that the values obtained for the potential 
sum in mixtures could be directly compared with those obtained for the 
same electrolytes in a pure solvent. The methods which have been 
adopted by investigators in this field, however, have consisted ess"entially 
in expressing the potential of an electrolyte in a mixture as a function 
of a single variable. This method consists in introducing a variable 
defined by an equation of the form: 

(108) C^=F{C„C,,...). 

This function is given such a form that the value derived for the poten- 
tial sum in the mixture, on introducing C^ as variable, corresponds with 

that of a solution of the pure substance when the same variable is intro- 
duced. If such a function exists, then we are led to conclude that the 
potential sum for a given electrolyte in solution is dependent, not upon 
the concentrations of the various substances involved, but upon some 
other single parameter. 

The potential of an electrolyte as a function of its concentration may 
be determined directly by means of the electromotive force of concentra- 
tion cells. More indirectly, the potential may be obtained from the 
vapor pressures of these solutions and from other related properties, such 
as the freezing point, boiling point, etc. If the experimental determina- 
tions are correct, the values of the potentials derived from the measure- 
ment of these different properties must necessarily be in agreement with 
one another. 

Lewis and Randall " have compared the available experimental data 
for aqueous solutions in this way, and have found them to be in excellent 
agreement. This implies the correctness of the methods employed in cal- 
culating the various thermodynamic quantities, as well as the accuracy 

i»« Lewis and Randall, J. Am. Chem. Soc. iS, 1112 (1921) 
"Idem, loc. dt. vj-^^j./. 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 331 

of the experimental methods, by means of which the data were secured. 
The practical application of thermodynamic principles to electrolytic 
solutions is largely due to G. N. Lewis.^^ In recent years numerous 
other writers have occupied themselves with this subject." The writers 
on this subject have commonly employed the activity function of Lewis/* 
which is defined by the equation: 

(109) M = RT log a + io, 

where a is the activity and io is a function independent of the concentra- 
tion of the constituent in question. The ratio of the activity of a sub- 
stance to its concentration is termed its activity coefficient and is thus 
defined by the equation: 

(110) ar=^. 

In a solution of an electrolyte we have an equilibrium of the type: 
n+^i* + n-Af = A', 

where A' represents a molecule of substance which dissociates into n* 
positively charged ions A^* and rf negatively charged ions A^'. The 
number of charges on the ions is not indicated. Introducing the values 
of M from Equation 109 in Equation 104 we may at once derive the 
expression: 

+n^ n- 

(111) log"—-^—=K, 

% 

where a*, a', and a denote the activities of the positive and negative 

ions and the un-ionized molecules, respectively, and Z is a function inde- 
pendent of concentration. For the change in the potential of the electro- 
lyte between any two concentrations of the system, we have the equa- 
tions: 

\ 

(112) (Sn'MOft- (2n'M')^ = RT log — , 

% 

(113) (2nM)j, — (2nM)^ = RT log 



^ a "■ a 



i2Lpw1s J Am. Chem. Soc. Si, 1631 (1912). , „, ,^ ^ ■ „, 

"BrSnsted /. Am. Chem. Soc. J,2, 761 (1920) ; BJerrum, Ztschr. f. Elektrochemie 21,, 

321 (1918) ; Ztschr. J. Anorg. Chem. 163, 275 (1920) ; Harned, J. Am. Chem. Soc. n, 

1808 J 1920).^^^^ Am. Acad. jS, 259 (1907) ; Ztschr. f. phys. Ch^m. 61, 129 (1907) ; ibid., 

10, 212 (1909). 



332 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

From Equation 112, the ratio of the activities of the un-ionized mole- 
cules for any two conditions of the solution may be determined if the 
potential change is known. Similarly, the ratio of the activity products 
of the ions may be determined from Equation 113. The actual value of 
the activity product is not in general determinable. At low concentra- 
tions, however, as is apparent from Equation 109, the activity a ap- 
proaches a value equal to that of the concentration C. If the potential 
can be determined at sufficiently low concentrations, that is, in solutions 
sufficiently dilute so that the laws of dilute solutions become applicable, 
the true values of the activity products may be determined. In systems 
in which a reaction takes place among the constituents the concentra- 
tions C are not usually determinable, so that the value of the true activity 
coefficients a remains undetermined. For practical purposes, therefore, a 
new activity coefficient has been introduced, defined by the equation: 

(114) a, = ^^, 

where C^ is the total concentration of the electrolyte. Further, instead 

of employing the values of the product of the activity coefficients, some 
function of the product of these coefficients is employed which makes the 
resulting coefficient more nearly comparable with that of a solution of a 
single molecular species. For electrolytes, Lewis and Randall have intro- 
duced a coefficient a , defined by the equation: 



(115) a 



(a+^ a-"") «" + "- 



a 



r 



(c/'^ Cg-"") »*+«- 



r 



where a^ and C^ may be called the reduced activities and the reduced 
concentrations of the ions." In a solution of a binary electrolyte: 

'•The nature of the various coefficients may be further elucidated by writine the 
equations for the potential sum in somewhat more explicit form. We have : * 

(117) l.nU = RTl.n log C + 2««„ + ■s.nj, 
where 

ZnJ = RT-Ln log ^, 

It is evident that this equation is not capable of being employed practicallv ft<i nn intor 
polation function, since C is not determinable. If, now, O is replac^ by ! the total 
salt concentration of the electrolyte in solution in pure water, *' 

(118) ^nM = RTZn log 0^ + Z»«„ + SnJ 

If the values of 7mM are known for different values of O , then the variation In the 
function SnJ^ over the concentrations in question is likewise known. In Equation 117 
ZnJ measures the change in the value of the potential of a siihsitiin^o i„ „ ,„„i „ ^ ' 
above that in an ideal system at the same conce^ntration. wSen"theTduc?d'coucent'?atlZ 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 333 



(116) 



«r = 



Ya+a~1 



V2 



'2 



Numerical Values. In comparing the thermodynamic behavior of 
different electrolytes, Lewis and Randall have compared the values of the 
reduced activity coefficients a^ at corresponding concentrations. In 
Table GXXX are given values of the activity coefficients of different 
electrolytes at a number of concentrations. These values have been 

TABLE CXXX. 

Activity Coefficients of Very Dilute Aqueous Solutions at 
Different Concentrations. 

O.OI 0.005 0.002 0.001 0.0005 0.0002 0.0001 

KCl, NaCl ... 0.922 0.946 0.967 0.977 0.984 0.990 0.993 

KNO3 0.916 0.943 0.965 0.976 0.984 0.990 0.994 

KIO3, NalOg . 0.882 0.915 0.946 0.961 0.972 0.982 0.988 

KjSO^ 0.687 0.749 0.814 0.853 0.885 0.917 0.935 

H2SO1 0.617 0.696 0.782 0.831 0.871 0.910 0.932 

BaClj 0.716 0.771 0.830 0.865 0.894 0.923 0.939 

C0CI2 0.731 0.784 0.840 0.873 0.900 0.927 0.943 

MeSO^ 0.40(4) 0.50 0.61 0.69 0.75 0.81 0.85 

K3Fe(CN)e .. 0.571 0.657 0.752 0.808 0.853 0.897 0.922 

La(N03)3 ....0.571 0.657 0.752 0.808 0.853 0.897 0.922 

derived from freezing point measurements and agree well with those 
derived by other methods. In Figure 59, the continuous curve represents 
the values of the activity coefficients of sodium chloride at different con- 
centrations as derived from freezing point determinations, while the 
points indicated by circles represent values of the coefiBcients as derived 

Og is introduced, 2«Jj measures this change of potential, together with the variation 
due to the substitution of C^ for 0. If we write : 

:ZnJ^ =RT'Zn log u,^ 

and introduce this function into the equation for the activity, we have : 
whence : 



BTSn log a = BTZn log C^ + RT Zn log 



2» log Og = S» log— • 



This equation defines the stoichiometric activity coefficient of Bronsted. If salts were 
completely ionized, the coeflicient a^ =a/0^ would be a measure of the true activity 
coefficient Since potential measurements yield values of the activity products only, an 
assumption is necessary if the activity coefficient is to be defined by means of an equation 
of the form : 



='C^)^ 



In mixtures of any number of electrolytes the definition of the total salt concentration 
also becomes uncertain and a further assumption of an arbitrary nature is involved in 
defining the activity coefficients. 



334 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

from electromotive force determinations.i^^ It is evident that the 
activity coefficients, as determined by the two methods, are in remark- 
ably good agreement. This indicates the correctness of the methods em- 
ployed in the calculations, as well as the accuracy of the experimental 
data. Similar calculations have been made for aqueous solutions of 



1.0 






















O 0.5 






Activity 

o 
o 













Fig. 59. 



0.0 0.5 1.0 1.5 3.0 Zi 

Square Root of Concentratioa. 

Activity Coefficients of Sodium Chloride Solutions as a Function of 
Concentration. 



sulphuric acid by the freezing point, electromotive force, and vapor pres- 
sure methods. Here, again, the results of the different methods have 
been found to be in excellent agreement. In Table CXXXI are given 
values of the activity coefficients of typical electrolytes at higher con- 
centrations. 

TABLE CXXXI. 



Activity Coefficients op Typical Electrolytes. 



HC1(25°) .. 
LiCl(25°) .. 
NaCl(25°) . 
KC1(25°) .. 
KOH(25°) . 

KNO3 

AgNO, 

KIO3, NalOa 

BaCl^ 

CdCl2(25°) . 

K,SO, 

H2SO,(25°) 
La(N03)3 .. 

MgSO, 

CdSO, 

CuSO, 



0.01 

0.924 

0.922 

0.922 

0.922 

0.92 

0.916 

0.902 

0.882 

0.716 

0.532 

0.687 

0.617 

0.571 

0.404 

0.404 

0.404 



0.02 0.05 0.1 



0.894 

0.892 

0.892 

0.892 

0.89 

0.878 

0.857 

0.840 

0.655 

0.44 

0.614 

0.519 

0.491 

0.321 

0.324 

0.320 



0.860 

0.843 

0.842 

0.840 

0.84 

0.806 

0.783 

0.765 

0.568 

0.30 

0.505 

0.397 

0.391 

0.225 

0.220 

0.216 



0.814 

0.804 

0.798 

0.794 

0.80 

0.732 

0.723 

0.692 

0.501 

0.219 

0.421 

0.313 

0.326 

0.166 

0.160 

0.158 



0.2 

0.783 

0.774 

0.752 

0.749 

0.75 



0.5 

0.762 

0.754 

0.689 

0.682 

0.73 



1 
0.823 
0.776 
0.650 
0.634 
0.75 



3 
1.35 
1.20 
0.704 



0.655 0.526 0.396 



0.244 
0.271 
0.119 



0.178 0.150 1.70 



0.110 0.067 



""AUmand and Polack, Jour. Clwm. Soc. US, 1020 (1919). 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 335 

As may be seen by reference to Table CXXX, the activity coefficients 
of electrolytes of the same type do not differ greatly at low concentra- 
tions. The activity coefficient increases as the concentration decreases 
at low concentrations. In solutions of strong acids and bases and of the 
alkali metal chlorides, the activity coefficients pass through a minimum 
at high concentrations. This, however, does not appear to be a general 
property of electrolytes, since silver nitrate does not exhibit a minimum 
up to concentrations of 5 molal. The higher the type of salt, the more 
rapidly does the activity coefficient decrease with increasing concentra- 
tion. While, as a rule, salts of the same type exhibit the same values 
of the activity coefficients, a number of exceptions occur, such as cadmium 
chloride, whose activity coefficient at 0.1 M is 0.219, while that of barium 
chloride at the same concentration is 0.50. Aqueous solutions of electro- 
lytes are remarkable for the uniformity of the phenomena presented. 
At low concentrations, many properties of these solutions differ only in- 
appreciably for different electrolytes of the same type. The same rela- 
tion is found in the case of the activity coefficients. At higher concen- 
trations, however, different electrolytes exhibit considerable variations. 

At low concentrations, the values of the reduced activity coefficients 

-^ approach those of the ionization coefficient y = -r-. The significance 
Cg Ao 

of this result is uncertain, since, even at the lowest concentrations, aqueous 
solutions of strong electrolytes do not conform to the requirements of 
the law of mass action. 

A comparison of the activity coefficients of solutions of pure electro- 
lytes with those of mixtures cannot be effected without some further 
assumption. A priori, we should not expect the activity coefficient of a 
given salt in a mixture of electrolytes to correspond closely with that 
in a solution of the pure substance. From Harned's measurements on 
the electromotive force of concentration cells with mixed electrolytes, 
Lewis and Randall draw the conclusion that "in any dilute solution of a 
mixture of strong electrolytes, of the same valence type, the activity 
coefficient of each electrolyte depends solely upon the total concentra- 
tion." Where the mixture contains salts of different valence types, they 
have introduced a new concentration function defined by the equation: 

(119) C^ = 2 , 

where C is the total molal concentration of an ionic constituent in the 
solution and v is the number of charges which it carries. This quantity, 



336 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

C^, which is termed the ionic strength, is employed to express the activity- 
coefficient of a salt in a mixture in terms of a single variable. From their 
results they conclude that "in dilute solutions the activity coefficient of 
a given strong electrolyte is the same in all solutions of the same ionic 
strength." 




0.1 0.2 0.3 0.4 0.5 

Square Root of Ionic Strength, C 'A 

Fig. 60. Variation of 1/Cr for Thallous Cliloride as a Function of the Ionic 

Strength, C„%. 



In Figure 60 are represented values of the reciprocal of the mean 
molality of thallous chloride, defined according to Equation 115, against 
values of the square root of C^, defined according to Equation 119. In 

Table CXXXII are given values of the activity coefficients of thallous 
chloride as determined from solubility experiments. 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 337 

TABLE CXXXII. 
Activity Coefficients op Thallous Chloride in Mixtures at 25°. 



^m 


In KNO3 


InKCl 


InHCl 


In T1N( 


0.001 


0.970 


0.970 


0.970 


0.970 


0.002 


0.962 


0.962 


0.962 


0.962 


0.005 


0.950 


0.950 


0.950 


0.950 


0.01 


0.909 


0.909 


0.909 


0.909 


0.02 


0.872 


0.871 


0.871 


0.869 


0.05 


0.809 


0.797 


0.798 


0.784 


0.1 


0.742 


0.715 


0.718 


0.686 


0.2 


0.676 


0.613 


0.630 


0.546 



As may be seen from the figure, the curves, connecting the reciprocal of 
the mean reduced concentration -^ with the ionic strength, diverge 

largely at higher concentrations. With electrolytes of the same type, 
such as potassium chloride and hydrochloric acid, the divergence is not 
large. With potassium nitrate, however, the divergence at higher con- 
centration is marked, as is also that for the ternary electrolytes, barium 
chloride, thallous sulphate, and potassium sulphate. In view of the fact 
that these curves necessarily pass through a point corresponding to a 
saturated solution of pure thallous chloride, the conclusion of Lewis and 
Randall that the curves become coincident at lower concentrations is 
open to doubt, for it is conceivable that, since the curves exhibit a 
marked curvature at higher concentration, such curvature may be main- 
tained in mixtures at lower concentration. 

Lewis and Randall have also examined the solubility curves of higher 
types of salts, and have shown that, for limited concentration intervals, 
their principle of mixtures is able to account for the observed phenomena 
quite closely. 

Solubility Relations According to Bronsted. Bronsted^^ has also 
treated the solubility relations of mixtures of electrolytes.^^" He assumes 
that the van't Hoff factor i may be expressed as a function of the con- 
centration by means of the equation: ^^'' 

(120) 2 — ^ = xC^/^ 

" Bronsted, loo. cit. , ^ . , 

"» BTOnsted's theory of the solubility effects In mixtures of electrolytes is simply 
interpreted in terms of Bjerrum's theory of electrolytic solutions. Bjerrum assumes that 
electrolytes are completely ionized and that the observed effects are due to interaction 
between the ions. So far as the experimental foundation of Bjerrum's theory is concerne<l, 
however, It Is based chiefly upon observations in mixtures of electrolytes. JNaturaliy, 
Bjerrum's theory, in the case of a solution of a pure electrolyte, is in harmony with that 
of Mllner. See Bjerrum: D. Kgl. Danske Vidensk. Selsk. Skrifter (7), i,l (190o) ; Proc. 
fth Intern. Congr. Appd. Chem., Sect. X (1909) ; Ztschr. f. Mectroch. X7, 392 (1911) ; »Oid., 
gi, 321 (1918). 

lauNoyes and Falk, J. Am. Chem. Soc. SZ, 1011 (1910). 



338 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

where C is the molal concentration and 5t is a constant characteristic of 
the salt. Combining this empirical equation with the differential thermo- 
dynamic equations and integrating, he obtains the equation: 

(121) log C'C = 2kC jV3 -I- Const., 

where C. is the total salt concentration of the saturated solution. In 
the case of salts without a common ion, Bronsted assumes: 

where C^ is the total concentration of the saturating salt. This leads to 

the equation: 

C 

(122) log ^ = x(CjV3_ (7^^1/3). 

For the solubility of a salt in a mixture containing a salt with a common 
ion, Bronsted assumes: 

C' = Cg and C":=C^, 

where C and C" are the concentrations of the uncommon and the com- 
mon ion respectively. This leads to the equation: 

C C 

(123) log ^ = 2x (Cj V3 _ c^^V3) , 

These equations express the solubility of the saturating salt in terms of 
the total concentration of 'all the salts in solution. The value of the 
constant k depends upon the type of salt. For uni-univalent salts, 
Jt = approximately 1/3; for bi-bivalent salts, 4/3; and for tri-trivalent 
salts, 3. Bronsted shows, in the first place, that the form of the curve is 
determined by the values of the constants C^ and x. In the presence of 
salts without a common ion, the solubility of the saturating salt is in- 
creased due to addition of the second electrolyte; and this increase is the 
greater, the greater the value of the constant x. Moreover, the relative 
increase of the solubility is the greater, the smaller the value of C . In 
the presence of salts with a common ion, the form of the solubility curve 
depends upon the number of charges on the ions and the number of ions 
resulting from the different salts. Bronsted shows that solubility curves 
will, in general, exhibit a minimum. In the case of uni-univalent salts, 
this minimum will lie at very high concentrations; for bi-bivalent salts^ 
assuming k = 4/3, the minimum concentration is 0.12 m; and for tri- 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 339 

trivalent salts, assuming x = 3, the minimum is at 0.01 m. Bronsted's 
equations therefore account for the solubility relations of various salts 
in a general way, including the minima which have been observed in the 
case of salts of higher type. Adjusting the value of the constant x to 
represent the experimental values in the best possible manner, Bronsted 
has shown that his equations account for the observed solubilities up to 
0.1 N, practically within the limits of experimental error. 

According to Bronsted's equation, the activity of all salts ultimately 
passes through a maximum. Under these conditions, the solutions will 
be unstable at the maximum point and the system in these regions should 
separate into two liquid phases. In the case of salts of higher type, the 
concentration at which this phenomenon should occur lies in regions 
where the concentration is fairly low. Bronsted has actually been able 
to observe separation of a liquid phase in solutions of salts of certain 
trivalent ions. 

The results obtained, on comparing the thermodynamic potential of 
electrolytes in aqueous solution, show that these values as derived by 
different methods are in excellent agreement. Thermodynamic principles 
alone are not capable of supplying information as to the nature or number 
of the molecular species present in electrolytic solutions. The results are 
naturally in agreement with the assumption that electrolytes are com- 
pletely ionized and, in view of the fact that in the thermodynamic treat- 
ment we are restricted to total concentrations and not to actual concen- 
trations, the results are most simply interpreted on the basis of this 
hypothesis. This, however, does not preclude the possibility that un- 
ionized molecules or intermediate ions may exist, or, indeed, that other 
complexes may be present in these solutions. 

3. Theories Taking into Account the Interionic Forces, a. Theory 
of Malmstrom and Kjellin. A great many investigators have attempted 
to account for the properties of solutions of electrolytes by taking into 
account the forces acting between the charges. According to this view, 
as was pointed out by Thomson " and by Nernst,"^ the ionization of an 
electrolyte under given conditions should be the greater the greater the 
dielectric constant of the medium. 

Among those who have attempted a solution of the problem by this 
method are Kjellin ^^ and Malmstrom.^'' These theories, which are prac- 
tically the same, lead to an equation of the form: 

A log C- = log £ + log C^ + BCi'/' 

"Thomson, Phil. Mag. [5], 36, 320 (1893). 
"«Nemst, Ztschr. f. phya. Chem. IS, 531 (1804). 
"Kjellin, Ztschr. /. phys. Chem. 11, 192 (1911). 
" Malmstrom, see Kjellin, above. 



340 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 
where A, B and K are constants and C^ and C^ are the concentrations of 
the ions and the un-ionized molecules, respectively. For binary electro- 
lytes A has a value of approximately 1.5, B of 0.3 and K of 1.0. Applied 
to aqueous solutions of sodium and potassium chlorides, this equation 
was found to reproduce the results quite closely up to 0.05 N, the con- 
stants of the equation being fitted to the experimental values. Similar 
results were obtained with a number of ternary salts. The equation is 
not applicable to solutions in solvents of lower dielectric constant such as 
ammonia, even at low concentrations. At high concentrations, in sol- 
vents of dielectric constant less than 20, it is obviously inapplicable, 
since, according to this equation, A necessarily increases with concentra- 
tion. It may be noted that the form of this equation resembles somewhat 
that of Bronsted's for the solubility of a salt in the presence of other 
salts. 

b. Theory of Ghosh. The most comprehensive theory which has 
been proposed to account for the behavior of solutions of electrolytes is 
that of Ghosh.^° Ghosh assumes that strong electrolytes are completely 
ionized, but that only those ions whose energy is sufficiently great to over- 
come the electrostatic field due to the charges are active in carrying the 
current. It is difficult to see how Ghosh's activity coefficient differs from 
the usual ionization coefficient. Apparently, what this author has in 
mind is that the ionic complexes persist in the neutral molecules. While 
such an assumption is not fundamental to the older ionic theory, it is 
nevertheless true that previous investigators ^^ in this field have long 
since recognized that in the neutral molecule the identity of the ionic 
complexes is not lost. The theory of Ghosh, as well as those of some 
other writers, would be more readily understandable to most readers if 
the customary nomenclature had been retained. 

Ghosh calculates the potential due to the field on the assumption that 
the ions are distributed in the medium in a definite manner forming a 
space lattice. He assumes that the space lattice of a salt in solution 
corresponds to that of the salt in the crystalline state and therefrom cal- 
culates the distance between the positive and negative charges. In 
calculating the potential, Ghosh assumes that the ions form doublets so 
that the work involved in separating the ions is due only to the N pairs 
of positive and negative ions. This theory has been criticized by Part- 
ington,^2 Chapman and George,^' and more recently by Kraus.^* These 

=» Ghosh, Trans. Chem. Soc. 113, 449, 627, 707 790 (1918) 
(1907^°^'^^' '^'*"'^""*' Solutions at High Temperatures, Carnegie Publication No. 63, p. 350 
23 Partington, Trans. Faraday Soc. IS, 111 (1919-20) 
=» Chapman and George, Phil. Uag. n, 799 (1921) 
'<■ Kraus, J. Am. Chem. Soc. iS, Dec, 1921 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 



341 



criticisms need not be further considered here but it may be of interest to 
compare the conductance values calculated according to Ghosh's theory 
with those experimentally determined. 

For the conductance of an electrolytic solution Ghosh's theory leads 
to the following equation: 



(124) 
where 
(125) 



log A = log Ao - 



DT 



^ 



2.3026 mJ? " 



Here N is Avogadro's number, 6.16 X 10^^, E is the electrostatic unit of 
charge, 4.7 X 10"" E.S.U., R is the value of the gas constant in absolute 

Ci, Epiehlorhydrin. 

o.a o.os Aio o.is o.to o.as 

i.oo 



I. IB 



- 1-76 



2.16 


- 


1 ' 1 — 


1 1—' 1 1 


a.i* 


- 




\ 


a.iz 






\ 


iS"> 






\ 


1 

"^2.06 


V 


\ 




Z.ez 


■ 


\ 


\\ ■ 


2.00 


- 


\\ 


\\ - 


i.9d 




,w 


A 



/.74 


^ 




^ 


I.IZ 


^ 




o 




7i 


llo 










p. 




W 


/.6» 


<! 




(in 




o 


I.6& 


h-l 



/.*♦• 



/.€2 



OS 0.1- 0.6 0.e 1.0 I.Z /.* 1,6 1-0 

C*, Water. 

Fig 61 Plot of Ghosh's Conductance Function for Solutions of Potassium Chloride 
in Water at 18° and Tetraethylammonium Iodide in Epichlorhydrm at 25 . 

units and m is a factor depending upon the number of ions n resulting 
from the ionization of the neutral molecules and upon the number of 
charges associated with a single ion, as well as upon the manner of dis- 
tribution of these ions in the solvent medium. It is evident that, for a 



342 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

given solvent at a given temperature, the logarithm of the equivalent con- 
ductance is a linear function of the cube root of the concentration and 
Ghosh's theory may be readily tested by plotting the experimentally 
determined values of log A against those of C^'. If the equation is 
applicable, the experimental points should lie upon a straight line from 
which the values of Ao and p may be determined. If the equation is not 
applicable, the experimental points will evidently show a systematic 
deviation from a straight line. 

In Figure 61 are shown the curves for potassium chloride in water and 
for tetraethylammonium iodide in epichlorhydrin. It is evident from' 
the figure that the experimental points lie upon a curve concave toward 
the axis of concentrations at low concentrations and convex toward this 
axis at higher concentrations, with an inflection point between. The 
experimental points show a systematic deviation from a linear relation 
and Ghosh's equation therefore is not applicable. In Table CXXXIII 
the observed and calculated conductance values are compared. 

TABLE CXXXIII, 

COMPAEISON OF ObSEEVED AND CALCULATED VALUES OF A FOE KCl 

IN Watee at 18°. 
A„ = 132.06 p = 3.620 X 10' T = 291 D = 81 

V 5X10* 2X10* 10* 5X10' 2X10' 10' 5X10' 

Aeaic 130.80 130.35 129.90 129.35 128.40 127.47 126.30 

A-bs' 129.51 129.32 129.00 128.70 128.04 127.27 126.24 

Aobs."caic. ... — 1.39 —1.03 —0.90 —0.45 —0.36 —0.20 —0.06 

V 2X10" 10" 50 20 10 5 2 1 

Acaic 124.31 122.37 119.97 116.9 112.1 107.4 99.7 92.7 

Aobs' 126.24 122.37 119.90 115.6 111.8 107.5 101.3 96.5 

A„bs."-oaic. . +0.03 ±0.00 —0.07 —0.3 —0.3 —0.1 +1.6 +3.8 

The experimental values have a relative precision not less than 0.05 
per cent. It is evident, from the table, that the theoretical values deviate 
from the experimental values far in excess of any conceivable experimen- 
tal error, except at a few points in the immediate neighborhood of the 
inflection point, which is at about 0.01 normal. As may be seen from 
the curve for eptchlorhydrin, the deviations in this solvent are much 
greater than in water. It is to be noted, too, that the experimental points 
again lie upon a curve which is of the same type as that of potassium 
chloride in water ; that is, the curve is concave toward the axis of concen- 
tration at low concentrations and convex toward this axis at high con- 



THEORIES' RELATING TO ELECTROLYTIC SOLUTIONS 343 

centrations. It has been shown that this form of the curve is general and 
that in solutions of non-aqueous solvents the deviations from Ghosh's 
equation are much greater than in water, and therefore are far in excess 
of any possible experimental error.^' 

Ghosh has likewise treated other properties of electrolytic solutions. 
In view of the fact that his theory fails to account satisfactorily for the 
relation between the conductance and the concentration of electrolytic 
solutions, it is unnecessary to consider these properties here. 

c. Milner's Theory. Of the various theories proposed to account for 
the properties of electrolytic solutions, that of Milner is perhdps the most 
noteworthy, since it is comparatively free from arbitrary assumptions. 
Milner ^^ has calculated the virial for a system of positively and nega- 
tively charged particles by statistical methods, and therefrom has calcu- 
lated the influence of the ions on the freezing point of solutions.^""' He 
found, in effect, that the virial of a system of charged particles has a 
finite value, from which the osmotic pressure of the solution may be 
deduced, and therefrom the freezing point. 

In the following table are given values of the van't Hoff factor i for 
potassium chloride in water calculated by Milner, together with the values 
of i determined by Adams directly from freezing point measurements. 

TABLE CXXXIV. 

Comparison of Milner's Values op i, with Those Experimentally 

Determined. 

C 0.005 0.01 0.02 0.05 0.1 

Milner 1.962 1.947 1.926 1.885 1.838 

^Adams 1.961 1.943 1.922 1.888 1.861 

As may be seen from the table, the calculated values of i are in excel- 
lent agreement with those determined by Adams. Milner's values are 
based on the assumption that the electrolyte is completely ionized, the 
observed freezing point depression being due entirely to the interaction 
of the ions. If an ionization value were assumed corresponding to that 
given by the ratio A/Ao, the values of i, as calculated by Milner, would 
be lower than those observed. Milner has accordingly suggested that, 
within these ranges of concentration, strong electrolytes are completely 
ionized. If this is so, the change in the conductance of electrolytes must 

=»Mlfner, P^rW. «3, 551 (1912) ; ihid., 25, 742 (1913). 
Ma Compare, Cavanagh, Phil. Mag. iS, bOG (1922). 



344 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

be due to a reduction in the mean carrying capacities of the ions at higher 
concentrations. 

Thus far, the conductance of electrolytic solutions as a function of 
their concentration has not been accounted for with equal success. Mil- 
ner ^^ has considered this problem, but without arriving at an expression 
for the conductance as a function of concentration. He has concluded, 
however, that the decrease of conductance at low concentration must be 
mainly due to a decrease in the ionic mobilities and not to a decrease in 
their number. The argument here does not appear to be altogether con- 
vincing. Milner assumes, for example, that the undissociated molecules 
are normal in their osmotic behavior. The justification for this assump- 
tion is by no means obvious. Moreover, experimental facts weigh heavily 
against the generality of the conclusion reached. Weak electrolytes in 
water, and, apparently, all classes of electrolytes in non-aqueous solu- 
tions, approach the mass-action law as a limiting form at low concentra- 
tions. The difiiculty is not alone to account for the failure of the mass- 
action law in solutions of strong electrolytes in water but, also, to account 
for the applicability of this law to solutions in other solvents where, judg- 
ing by the lower value of the dielectric constant, the interionic forces are 
much greater than in water. Furthermore, according to Milner's theory, 
different electrolytes in dilute solutions should exhibit practically identi- 
cal properties both as regards their osmotic and their electrical properties. 
This condition is approximately fulfilled in water, but not in solutions in 
non-aqueous solvents. In these latter solvents, the electrolyte appears 
to retain its individuality even at exceedingly low concentrations. Any 
theory which cannot give an account of this fundamental property of 
electrolytic solutions is obviously incomplete. 

It is not difiicult to see in what manner the conductance would be 
influenced by interionic action at higher concentrations. According to 
Milner, the ions are not distributed haphazard throughout the medium, 
but, on the average, as the result of interaction between the charges, ions 
having like charges are somewhat farther apart and ions having unlike 
charges somewhat nearer together than would otherwise be the case. 
Ordinarily it is assumed that a charged particle moves in a uniform 
electric field. If, however, the ions are combining and dissociating, or, 
in any case, if charged particles approach each other sufficiently closely, 
the surrounding field will be influenced and the speed of the ions will vary 
for different individuals, depending upon the proximity of other ions. 

According to this view, the ratio y = -r- is a measure, not of the number 

"Milner, PMl. Mag. SS, 214 and 352 (1918). 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 345 

of particles actually engaged in the transport of the current, but of the 
mean conducting power of the ions. It does not necessarily follow, how- 
ever, according to this view, that all the ions in solution are at all times 
acting as carriers of the current. 

Lewis and Randall ^^ have recently pointed out that the ionization of 
an electrolyte cannot be defined without some degree of arbitrariness. 
This difficulty is not one confined to electrolytic solutions. In all sys- 
tems, in which reaction takes place among a number of constituents 
throughout the mass of the mixture, the definition of the concentration 
of the various constituents concerned becomes uncertain. So long as the 
system is dilute, the concept of concentration is definite; but, when the 
concentrations reach such values that the forces acting between the con- 
stituents become appreciable, the concept embodied in the term molecule 
becomes indistinct. This difficulty arises of necessity whenever we pass 
from the purely thermodynamic to the kinetic method of treating systems 
of real substances. That these various difficulties should arise in solu- 
tions of electrolytes is not surprising, since these are the only concentrated 
systems regarding which we have data sufficiently accurate to enable us 
to observe the deviations from ideal systems with any considerable degree 
of certainty. That un-ionized molecules exist in aqueous solutions of 
ternary salts in water appears to be conclusively demonstrated by the 
fact that transference measurements have shown that complex cations 
exist. Thus, the transference number of the cadmium ion, in cadmium 
iodide, according to Hittorff, is greater than unity at high concentrations, 
and the manner in which the transference number of cadmium chloride 
varies with the concentration indicates that its behavior is not essentially 
different from that of cadmium iodide. It must be assumed, therefore, 
that, in solutions of cadmium salts, ions of the type CdX+ exist. If this 
is true of one electrolyte, the same may well be true of others. 

Finally, it is not sufficient that a theory of electrolytic solutions shall 
account merely for a diminution in the conducting power of electrolytes 
with increasing concentration, for, in solutions in non-aqueous solvents, 
the conductance increases with increasing concentration at higher con- 
centrations; and, if the dielectric constant is sufficiently low, the con- 
ductance increases with increasing concentration even at relatively low 
concentrations. 

d. Hertz's Theory of Electrolytic Conduction. P. Hertz ^^ has at- 
tempted to solve the problem of electrolytic conduction by taking into 
account the interionic forces. He has derived the following equation 

"LOC. cit. 

» Hertz, Ann. d. Phys. S7, 1 (1911). 



346 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

expressing the relation between the equivalent conductance A and the 
concentration C of the solution: 

(126) xHu) =u^\\^-Si{u)Y+ [Ci{u)r^ 

where 

u 

(127) Si{u)=\^^^-^du, 



u 



(128) Ci{u) = ^^-^du, 



(129) ■iJ,(m)=B(A„ — A), 
and 

(130) u = AC^/^ 

Here Ao, A and B are constants. Ao is the limiting value which the 
equivalent conductance approaches as the concentration decreases indefi- 
nitely. This equation is of the form: 

(131) B(Ao — A) =il)(AC^/^). 

It is evident that, for a given solvent under given conditions, the 
conductance function will have the same form for different electrolytes 
according to this theory. If the values of \|) (u) and of u are represented 
graphically, then it should be possible to transform the curve for one 
electrolyte into that for another by merely altering the scale of plotting. 
It is obvious that this condition will be very nearly fulfilled in aqueous 
solutions of strong binary electrolytes, since the ionization of different 
electrolytes at lower concentrations is practically identical. If Hertz's 
theory held strictly, the value of the constant A would be predetermined 
by the nature and condition of the solvent and would be independent of 
the nature of the electrolyte. The difference in the values of the con- 
ductance of different electrolytes, therefore, would be accounted for by a 
difference in the values of the constants Ao and B, and the different con- 
ductance curves should be transformable one into the other by merely 
altering the values of these constants; or, if Ao is otherwise determined, 
by merely altering the value of the constant B. 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 347 

Lorenz '" has tested the applicability of Hertz's function to aqueous 
solutions of binary electrolytes and has concluded that this function is 
applicable. As has just been pointed out, this was to have been expected. 
It should be noted, however, that the value of A, according to Lorenz, 
differs appreciably for different electrolytes. This result may, in part, 
be due to the fact that the function has been applied at concentrations 
where the viscosity effects become appreciable. 

It is evident that Hertz's fimction will not be generally applicable 
to solutions in non-aqueous solvents, certainly not unless the value of 
A is assumed to differ largely for different electrolytes. Furthermore, it 
will be entirely inapplicable to solutions in non-aqueous solvents of low 
dielectric constant at higher concentrations. It is evident from Equation 
126 that the factor of u^ is essentially positive so that Aq — A must 
necessarily increase with increasing concentration. It is known, however, 
that, in solvents of low dielectric constant, the value of A passes through 
a minimum, after which the value of Ao — A decreases with increasing 
concentration. This theory, like others of its kind, is at best restricted 
in its applicability. As yet it has not been compared with experimental 
data in a sufficient number of solutions to make it possible to form a 
clear opinion as to the range of its applicability. In any case, it is in- 
applicable to solutions in solvents of very low dielectric constant, even 
though these solutions may be dilute. Here again, as in the case of 
Milner's theory, the difference in the behavior of strong and weak elec- 
trolytes remains to be accounted for. 

4. Miscellaneous Theories. A great many other theories have been 
suggested to account for the behavior of electrolytic solutions. In gen- 
eral, these theories have not been worked out sufficiently to comprehend 
within their scope more than a limited number of properties of a limited 
number of systems. Many of them, indeed, are purely qualitative in 
character. 

To account for the increase in the conductance of solutions of elec- 
trolytes in solvents of very low dielectric constant, Steele, Macintosh 
and Archibald ^^ have suggested that at higher concentrations the elec- 
trolyte polymerizes, and that only these polymerized molecules are capa- 
ble of ionization. They show that, if a sufficient degree of polymerization 
is assumed, an ionization curve is obtained somewhat similar in form to 
that of ordinary electrolytes in aqueous solution. Thus far, this theory 
is purely qualitative in character and an exact test of its applicability 
is therefore not possible. We should expect, however, that if only 

""Lorenz and Michael, ZtscJir. f. anorg. Cliem. 116, ICl (1921); Lorenz and Neu, 
ibid lie 45 (1921) ; Lorenz and Oaswald, ibid., lU,, 209 (1920). 
"'"•'n Steele, Macintosh and Archibald, Phil. Trans. [A] 205, 99 (1905). 



348 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

polymerized molecules were capable of ionization, intermediate ions 
would be present in solution and transference measurements with such 
solutions, therefore, should yield very abnormal values for the transfer- 
ence numbers. While certain transference numbers are unquestionably 
abnormal and while it is indeed very probable that polymerization often 
occurs in solutions of electrolytes in solvents of both high and low dielec- 
tric constant, it remains to be shown that the phenomenon is a general 
one and that it is capable of accounting for the observed properties of 
electrolytic solutions. Nevertheless, it is highly probable that the effect 
of polymerization will have to be taken into account in many cases at 
higher concentrations. It appears, however, that polymerization should 
lead to a lower rather than to a higher value of the conductance. Trans- 
ference measurements with the alkali metal halides in acetone yield 
abnormally high values for the cations, indicating the formation of a 
complex cation. It is to be noted, however, that the conductance of the 
halide is the lower the greater its tendency to form complexes. Thus, the 
conductance of lithium chloride in acetone at higher concentrations is 
much lower than that of potassium iodide or sodium iodide. That com- 
plex ions are formed in solutions of cadmium iodide in water was shown 
by Hittorf, as has already been pointed out. The assumed ionization 
process in solutions of electrolytes is in a large measure hypothetical. 
This may account for numerous discrepancies at higher concentrations. 

Other writers consider solutions of strong electrolytes to be similar 
to solutions of colloids. Among these are Reychler,^^ Georgievics ^^ and 
Wo. Ostwald.^* These theories, however, appear to be little more than 
analogous, based chiefly upon the similarity between the Storch equation 
and the adsorption equation. The Storch equation is only an approxima- 
tion in aqueous solutions which, in other solvents, fails entirely. The 
osmotic effects in solutions of electrolytes, also, are not in harmony with 
the view that solutions of strong electrolytes are colloidal in character. 

Some writers attempt to account for the properties of aqueous solu- 
tions by taking into account reactions between the solvent and the elec- 
trolyte. In this connection, it is to be noted that electrolytic solutions are 
not confined to solvents of the water type. Indeed, such solvents need 
not necessarily contain hydrogen and, in fact, may be elementary sub- 
stances, or neutral carbon compounds such as chloroform. In view of 
this fact, it is highly improbable that the properties of electrolytic solu- 
tions may be generally accounted for on the basis of chemical processes 

'2 Reychler, "Etude sur I'Equilibre de Dissociation," Brocbure No. 3 Bruxelles (1917) 
H. Lamertin. * \ >< 

" Georgievics, Ztachr. J. pltys. Ohem. W, 356 (1915) 
"Ostwald, Ztschr. Ohem. Ind. Koll. 9, 189 (1911). 



THEORIES RELATING TO ELECTROLYTIC SOLUTIONS 349 

taking place between the solvent and the dissolved electrolyte. But 
here, again, there are doubtless many instances where interaction between 
the electrolyte and the solvent or an added non-electrolyte is a primary 
factor in the ionization process, particularly at higher concentrations. 

5. Recapitulation. In recapitulation, solutions of strong electro- 
lytes, even at low concentrations, do not conform to the laws of dilute 
systems. The thermodynamic properties of these solutions can not, 
therefore, be employed for the purpose of determining the state of the 
electrolyte in these solutions. The conductance method might be ex- 
pected to give a measure of the fraction of the ionized and un-ionized 
molecules present. However, the fact that the relative conductance of 
the ions of strong acids varies at low concentrations renders the results 
of the conductance method doubtful. 

The hypothesis that electrolytes are completely ionized up to fairly 
high concentrations lacks experimental support. The agreement of the 
hypothesis with the consequences of thermodynamic principles can not 
be looked upon as lending material support, since thermodynamics can 
teach us nothing with regard to the molecular state of a system without 
a supplementary hypothesis which directly or indirectly involves the 
equation of state. The fact that the law of mass-action is approached 
as a limiting form in aqueous solutions of weak electrolytes and in non- 
aqueous solutions of all electrolytes for which reliable data are available 
indicates that, if strong electrolytes in aqueous solution are completely 
ionized, this constitutes only a particular case and the general problem 
still remains to be solved. 

Any theory which undertakes to account for the decreased conduct- 
ance of electrolytes at higher concentrations, on the assumption that the 
conductance change is due to a change in the speed of the ions, must 
likewise account for the fact that, in solvents of low dielectric constant, 
the conductance passes through a minimum value after which it increases. 
This point may lie at relatively low concentrations. 

The theories of electrolytic solutions thus far advanced are founded 
chiefly on observations relating to aqueous solutions. There is great 
danger, here, that phenomena may be assumed as general which, in fact, 
are only particular. It is of the greatest importance to analyze the 
results obtained from a study of the properties of solutions in various sol- 
vents in order to determine which of these are general, applying to all 
electrolytic solutions, and which are particular, applying only to solutions 
in certain solvents or under certain conditions. Aqueous solutions are 
characterized by the uniformity of the phenomena presented by different 
electrolytes. In other words, the electrolyte, in aqueous solution, has, 



350 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

in a large measure, lost its individuality. This is not true of solutions 
in other solvents. Here the electrolyte retains its individual character- 
istics even at very low concentrations. It is interesting to note that, at 
higher temperatures, certain of the individual properties of electrolytes 
in aqueous solution disappear while others make their appearance. Thus, 
the ionic conductances approach one another at higher temperatures, 
while the ionization values diverge the more the higher the temperature. 
It is not to be doubted that the properties of aqueous solutions at higher 
temperatures closely resemble those of non-aqueous solutions under 
ordinary conditions. 

It is not unlikely that, in the end, many of the theories, which have 
been suggested from time to time and found inapplicable, contain certain 
elements of truth. The error has been introduced in attempting to apply, 
generally, theories which are applicable only to special cases. It appears 
probable that, ultimately, it will be necessary to take into account, under 
various conditions, a change in the speed of the ions with concentration as 
well as a change in the degree of ionization. At the same time there will 
doubtless be found many cases in which intermediate ions are formed and 
in which the electrolyte polymerizes. Yet there is found, in all electro- 
lytic solutions, a certain unity among the phenomena, which indicates 
the existence of a comparatively small number of chief governing factors. 



Chapter XIII. 
Pure Substances, Fused Salts, and Solid Electrolytes 

1. Substances Having a Low Conducting Power. In the preceding 
chapters, the properties of solutions of electrolytes have been discussed. 
We shall now consider, briefly, the properties of pure substances in the 
liquid state. Nearly all substances in the fused condition exhibit a 
measurable, though often small, conducting power for the electric cur- 
rent. Even such substances which we ordinarily class as insulators con- 
duct the current in some degree. What the nature of the conduction 
process is in these substances has not been shown, but in all likelihood 
the process is an ionic one; that is, the current is carried by particles of 
atomic or molecular dimensions. A typical example of this class of con- 
ductors, or perhaps more properly insulators, is found in the hydrocar- 
bons. It has been shown that the conductance of substances of this type 
is materially affected by the presence of small amounts of impurities. 
The specific conductance of nearly all poorly conducting substances is 
materially decreased by careful drying and fractionation. Evidently, 
therefore, in part at least, the conductance of this class of substances is 
due to the presence of other substances, as a result of which their con- 
ductance is. materially increased. We have, however, no knowledge of 
the nature of the charged particles by means of which conduction is 
effected. 

In the case of petroleum ether and hexane, it has been found possible 
to carry the process of purification so far that the effect of impurities is 
almost entirely eliminated. It has been found that the residual con- 
ductance in these solvents is chiefiy due to the action of radiations from 
surrounding bodies, as a result of which the solvent itself is ionized.^ 
The conductance under these conditions was found to be altered by sur- 
rounding the conductance vessel with screens which absorb the external 
radiation. The conductance of pure hexane, therefore, is lower than that 
due to the ions produced by the radiation from surrounding bodies and 
it is possible that the conductance of this substance is in effect zero. 
Under ordinary conditions, the conductance of the hydrocarbons is due 
primarily to impurities. 

•Jaff«, Ann. d. Pfws. 32, 148 (1910). 

351 



352 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Recent investigations on the conduction process in solid dielectrics 
have disclosed the fact that in these media Ohm's law is not obeyed.'' 
The substances investigated were mica, glass, paraffin, shellac and cellu- 
loid. Excepting paraffin, for which the conductance was so low that the 
results were uncertain, the conductance was found to increase with the 
applied potential. The logarithm of the specific conductance increases 
approximately as a linear function of the potential gradient. In the case 
of mica, with which substance measurements were made over a large 
range of potential, the conductance curves are slightly concave toward the 
axis of potentials. In the case of glass the conductance increase at higher 
temperatures was found to be noticeably smaller than at lower tempera- 
tures. 

Since Ohm's law does not hold, it must be assumed either that the 
number of carriers increases with the applied potential or that the mean 
speed of the carriers increases. It is not improbable that, under the 
action of the applied potential, carriers of a type differing from those 
normally present in the dielectric medium may be formed. It is of par- 
ticular interest to note that in glass, which is an electrolyte at higher 
temperatures, the above mentioned results indicate a conduction process 
differing from that at higher temperatures. 

Compounds of hydrogen with elements which are strongly electro- 
negative are in general ionized to a slight degree. The most familiar 
example of this type is water itself, which in the pure state has a specific 
conductance in the neighborhood of 0.042 X 10"'.^^ Other hydrogen de- 
rivatives of strongly electronegative groups likewise appear to conduct 
the current in the pure state, some of them much more readily than 
water. The specific conductance of formic acid appears to lie in the 
neighborhood of 10-^ In these cases, however, the process of purification 
has not been carried to such a point that it can with certainty be stated 
that the residual conductance is entirely or chiefly due to the ionization 
of the solvent alone. In the case of hydrogen derivatives, in which the 
hydrogen is not joined to a strongly electronegative group, the residual 
specific conductance is as a rule relatively low and it is as yet uncertain 
to what the residual conductance is due. Acetone, for example, may be 
purified to a point where its specific conductance is of the order of 10"^ 
but whether this residual conductance is due to acetone itself or to some 
impurity is unknown. The same obviously holds true of solvents which 
contain no hydrogen, such as sulphur dioxide, bromine, etc. 

The hydrogen derivatives of the strongly electronegative groups are 

'Poole, PMl. Mag. 1,2, 488 (1921). 

"• KohirausclJ ana Heydwelller, Ann. d. Phys. 83. 209 (1894). 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 353 

perhaps to be classed as salts. In other words, these compounds should 
be classed, not with the ordinary hydrocarbons, but rather with the dis- 
tinctly salt-like substances. These derivatives, when dissolved in water, 
or other suitable solvents, yield solutions which conduct the current with 
great facility and which often form compounds with the solvent. Hydro- 
chloric acid forms a stable complex, ammonium chloride, with ammonia; 
and with water at low temperature it has been shown to form a complex 
HCl.HsO.^ In water itself, therefore, hydrogen and hydroxyl ions do 
not consist merely of a hydrogen atom and an OH group associated with 
the positive and negative charge respectively, but rather of complexes in 
which the solvent itself is involved. In a sense, therefore, water and 
ammonia and hydrogen chloride may be considered to be related to salts. 
However, the typical salts in a fused state exhibit in most instances a 
conductance much greater than that of the substances which we have 
just been discussing. 

With a few exceptions, fused salts conduct the current with extreme 
facility. Among these exceptions mercuric chloride is one of the most 
common and striking examples. This salt is itself an electrolytic solvent 
for other salts, while its specific conductance in the pure state is very 
low.* Correspondingly, solutions of mercuric chloride in other solvents, 
as for example water, appear to be only slightly ionized. This class in- 
cludes the organic tin salts of the type RgSnX. Trimethyltin iodide, for 
example, is a liquid at ordinary temperatures whose conductance is less 
than 4 X 10''. This salt when dissolved in water is ionized nor- 
mally.' 

2. Fmed Salts. Inorganic substances which are non-electrolytes in 
solution, in general, possess only a very low conducting power in the pure 
state. This, for example, is the case with boric oxide. On the other 
hand, oxides of the strongly electropositive elements appear to be con- 
ductors in the fused or even in the solid state. It is, however, the typical 
salts in their fused state which are of greatest interest. These substances, 
in general, conduct the current with extreme facility, by means of a 
purely ionic process, since, as has been shown, Faraday's law applies. 

In Table CXXXV are given values of the specific conductance [i of 
sodium nitrate at different temperatures, together with the equivalent 
conductance A as calculated from the known specific volume, the fluidity 

of the fused salt F, and the ratio of the conductance to the fluidity -^ .« 

= Rupert, J. Am. Chem. Soc. 31, 851 (1909). 

•Poote and Martin, Am. Chem. J. il, 45 (1909). . ,, , t i. 4. 

"Unpublished observations by Mr. C C Callis in the Author's Laboratory. 
•Goodwin and Mailey, Phys. Rev. 25, 469 (1907) ; iMd., 26, 28 (1908). 



354 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

TABLE CXXXV. 

Conductance and Fluidity op Sodium Nitrate at Different 
Temperatures. 

t n A F A/F 

350° 1.173 52.87 42.6 1.24 

400 1.384 63.59 54.0 1.18 

450 1.562 73.15 65.0 1.12 

500 1.716 81.94 77.2 1.06 

It will be observed that the specific conductance \i, as well as the equiva- 
lent conductance A, increases very nearly as a linear function of the tem- 
perature. Obviously, the equivalent conductance will vary nearly in 
proportion to the specific conductance, since the density of the fused salt 
varies only comparatively little with temperature. Between 350° and 
500°, the specific conductance increases approximately 60 per cent, which 
corresponds roughly to an increase of % per cent per degree. The fluidity 
varies somewhat more than the conductance over the same temperature 

interval, so that, as the temperature rises, the value of the ratio ^ de- 
creases. It is interesting to note that the value of -^ is near unity, which 

differs not greatly from the value of -^ for electrolytic solutions, par- 

r 

ticularly in the case of water. This may be taken to indicate that the 
fused salts are highly ionized. 

For different fused salts, the conductance is of the same order of 
magnitude, corresponding to the fact that they have approximately the 
same fluidity. In Table CXXXVI are given values of the specific con- 
ductance [I, the equivalent conductance A, and the fluidity F, together 

with the ratio r= for different salts. It will be observed that the ratio 
r 

TABLE CXXXVI. 

Values op A and F for Different Fused Salts. 

H A F A/F 

350°C. NaNOg 1.173 52.88 42.6 1.24 

" KNO3 0.6728 36.54 38.0 0.96 

" AgNOa 1.245 55.43 45.5 1.22 

310°C. LiNOg 1.126 44.21 27.2 1.62 

250° C. AgClOa 1.4743 27.72 

A / 

p is of the same order for the different salts. In the case of the nit rates 

the ratio is smallest for potassium nitrate and greatest for lithium nit,rate. 

The order of the ratio ^ corresponds to the order of the atomic voh'ames, 



PURE SUB^STANCES, FUSED SALTS, SOLID ELECTROLYTES 355 

Jaeger and Kapma^» have measured the specific conductance and the 
densities of potassium nitrate, sodium nitrate, lithium nitrate, rubidium 
nitrate, caesium nitrate, potassium fluoride, potassium chloride, potas- 
sium bromide, potassium iodide, sodium molybdate, and sodium tung- 
state over considerable temperature ranges. At a given temperature, the 
equivalent conductance of the different salts is of the same order of 
magnitude. For the nitrates the conductance increases in order from 
caesium to lithium. For the potassium halide salts, the conductance is 
smallest for the fluoride and greatest for the chloride, while that of the 
iodide and bromide is intermediate between them. 

The conductance increases very nearly, although not quite, as a 
linear function of the temperature. The temperature coefiicients vary 
appreciably, being greatest for potassium fluoride and smallest for 
caesium nitrate. 

The conductance of mixtures of fused salts is very nearly a linear 
function of the composition. In the following table are given values of 
the conductance of mixtures of sodium and potassium nitrates at 450°, 

together with the values of F and of ^.'^ It will be observed that as the 

r 

concentration changes the conductance varies continuously between that 
of the two components. 

TABLE CXXXVII. 
Conductance of Mixtures op Sodium and Potassium Nitrates at 450°, 

20 50 80 100 molar %KN03 

[1 .. 1.562 1.389 1.205 1.059 0.973 

A .. 73.15 67.84 62.56 57.96 55.03 

F .. 65.7 .. 66.3 63.3 60.2 " 

A/F .. 1.12 .. 0.945 0.915 0.915 

The fact that in the mixtures of fused salts the conductance is approxi- 
mately a linear function of the composition shows that no considerable 
reaction takes place on mixing. This indicates a high degree of ioniza- 
tion of the fused electrolyte. 

In Table CXXXVIII are given values of the conductance of mixtures 
of silver iodide and silver bromide at 550°.' Here, again, the conduc- 

TABLE CXXXVIII. 

Conductances of Mixtures of Silver Iodide and Silver Bromide. 

%AgBr 5 10 20 30 40 60 70 80 90 100 
(1.... 2.36 2.40 2.39 2.41 2.43 2.50 2.64 2.67 2.68 2.84 3.00 

""Jaeger and Kapma, Ztsclir. /. Anorg. Ghem. US, 27 (1920). 
'•Goodwin and Mailey, loo. cit. ,^„^,^ 

'Xubandt and Lorenz, Ztsclvr. f. phya. Ohem. 87, 543 (1914). 



356 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tance varies continuously between that of the two components. It is 
true that a few irregularities occur, but these are small and probably lie 
within the limits of experimental error. The fused salts are characterized 
by the great similarity in their behavior. As has already been pointed 
out, the order of magnitude of the conductance is the same for all typical 
fused salts. 

In the following table are given values of the conductance of thallium 
and silver salts at 600°.* 

TABLE CXXXIX. 

Conductance of Thallotjs and Silver Salts at 600°. 

Til 0.840 Agl 2.43 

TlBr 1.127 AgBr 3.08 

TlCl 1.700 AgCl 4.16 

In both cases, the conductance of the salt increases in the order: iodide, 
bromide, chloride. The conductance of the silver salts is markedly 
greater than that of the thallium salts. 

A great many data are available relating to the conductance of fused 
salts,' but, in view of the similarity in the behavior of the different fused 
salts, it is unnecessary to give here in detail the various observations 
which have been recorded. Thus far, the subject has been studied chiefly 
from an empirical point of view and we possess but little knowledge of 
the molecular condition of these substances. 

The form of the conductance curve of mixtures of sodium and potas- 
sium nitrate and of silver chloride, iodide and bromide indicates 
that in these mixtures complex ions are not formed. In some other in- 
stances, however, there is a probability that complex ions may exist.^° 
This is the case, for example, with mixtures of potassium chloride and 
lead chloride. Lorenz has carried out transference measurements which 
indicate that a complex of the type KjPbCl^ is probably formed in the 
mixture. 

3. Condiictance of Glasses. For want of a suitable reference sub- 
stance, transference measurements with the fused salts have not been 
carried out, and as a consequence we lack any knowledge as to the pro- 
portion of the current carried by the two ions in these electrolytes. In 
a few instances, however, particular systems have been investigated in 
which the current is carried entirely by either the positive or the nega- 

• Tubandt and Lorenz, loc. cit. 

"Lorenz, "Electrolyse geschmolzener Salze, Monographlen u. Angew. Blcctrocli," ?9 
(1905). 

"Lorenz, Ztechr. J. phye. CMm. 10, 830 (1910), 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 357 

tive ion. Among those substances which may be classed strictly as fused 
salts are the glasses. A glass is to be considered as a supercooled liquid 
which is mechanically rigid. Usually, glasses consist of mixtures of 
silicates of the alkali metals and the metals of the alkaline earths. What 
the nature of the compounds is in these systems is not known. Doubt- 
less, the silica is present in the electronegative constituent. It is well 
known that ordinary glasses are excellent conductors of the current at 
high temperatures, the conductance increasing with the temperature. In 
general, the conductance-temperature curve is exponential in form. 

In the following table are given values of the resistance of ordinary 
soda-lime glass at different temperatures.^^ 

TABLE CXL. 

Resistance of Oedinaey Soda Glass at Different Temperattjees. 

Temperature C... 325 355 404 469 484 500 540 
Resistance 9200 1900 687 172 133 89 2.4 

It will be observed that, even at temperatures as low as 325°, glass con- 
ducts the current with measurable facility, while in the neighborhood of 
its softening point, 540°, it conducts extremely well. To what the great 
increase in the conductance of glass is due is uncertain. We shall see 
below that the ionization of a glass varies only little as a function of the 
temperature and consequently the increased conductance must be due 
to the increased speed of the ions. The nature of the frictional resist- 
ance which the ions meet in their motion through a glass is, however, 
uncertain. At temperatures below 400°, glasses of this type appear to 
be entirely rigid and consequently the increased conductance is not 
simply related to the mechanical rigidity of the glass. 

The conduction process in the case of the glasses is electrolytic in 
character."* If a current is passed through a glass tube from a sodium 
nitrate anode to a mercury cathode, metal is transferred from the sodium 
nitrate to the mercury through the glass in accordance with Faraday's 
law and no change whatever takes place in the glass itself. This indi- 
cates that the conduction process in such glasses is due to the motion 
of the sodium ion and is not due to the motion of an electronegative ion. 
This type of conduction is characteristic of many rigid electrolytic con- 
ductors. Since positively charged carriers are present within the glass, 
it is obvious that negative carriers must likewise be present. The nega- 
tive carriers, however, must form a substantially rigid system, since they 
take no part in the conduction process. It is also evident that, in the 

n°L%^^TAn?ln^^'K«\'chb"a"Jl"l'S'c.V'TpW». CHen.. 7.. 468 (1910). 



358 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

case of the glasses, the ions consist of the atoms themselves, since, on 
passing a current through soda-lime glass, the only material transferred 
is sodium. This and similar cases are the only ones in which it has 
been definitely demonstrated that an electrolytic ion consists of a charged 
atom alone. 

In the case of glasses, it is possible to substitute the sodium ion by 
another positive ion.^^" Such a substitution is, in effect, a determina- 
tion of the speed of the ions by the moving boundary method. Substitu- 
tion may be quite generally effected but, in the case of most positive ions, 
the glass disintegrates as the process proceeds. In the case of silver, 
however, a substitution may be carried out to a considerable depth. If 
sodium is substituted by silver, the weight of the glass is increased in 
proportion to the difference in the atomic weight of silver over that of 
sodium. In the following table are given values of the gain in weight 
of a sample of soda glass, together with the values calculated from the 
amount of electricity passed as determined in a coulometer.^^" The tem- 
perature is given in the first coliunn. 

TABLE CXLI. 

Obsesved and Calculated Gain in Weight of Soda Glass on 
Substitution by Silver. 

Gain in Weight Gain in Weight 
Temperature Calculated Observed 

350° 0.0339 g. 0.0347 g. 

350° 0.0396 0.0416 

343° 0.0732 0.0762 

343° 0.0209 0.0209 

By measuring the penetration of the silver boundary into the glass 
under a given potential gradient, it is possible to determine the volume 
of the glass which has been affected, and, knowing the composition of 
the glass, it is possible to determine the fraction of sodium in the glass 
replaced by silver. This has been done in the case of soda glass with 
the following results.^^" 

TABLE CXLII. 

Relative Amounts of Sodium Replaced by Silver in Soda Glass. 

t Y% 

278° 76.5 

295° 76.8 

323° 77.05 

343° 82.3 

"^Heydwelller and Kopfermann, Ann. d. Phya. SS, 729 (1910). 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 359 

While these values are not very precise, nevertheless, they clearly indi- 
cate that about three-fourths of the sodium present in these glasses may 
be electrolyzed out and replaced by another metal. The effective ioniza- 
tion of the sodium in soda glass, therefore, is of the order of magnitude 
of 75 per cent. This is apparently the only direct determination which 
has thus far been made of the relative amount of a substance actually 
concerned in the conduction process in an electrolyte. If so large a 
proportion of the sodium in soda glass is actually concerned in the con- 
duction process, it is reasonable to assume that the fused salts are very 
nearly completely ionized. It is interesting to note that, as the tempera,- 
ture rises, the ionization of sodium in glass increases slightly. 

Since the penetration of the silver is determined solely by the rate 
of motion of the ions and since the conduction is due entirely to the posi- 
tive ion, it follows that the depth of penetration should be proportional 
to the specific conductance or inversely proportional to the specific resist- 
ance of the glass. This condition is in general fulfilled. 

From the preceding data it is possible to calculate the speed of the 
sodium ion in glasses ; that is, the speed with which this ion moves under 
a potential gradient of one volt per centimeter. In the following table 
are given values of the absolute speed of the sodium ion at different 
temperatures. 

TABLE CXLIII. 

Absolute Speed of the Sodium Ion in Soda Glass at Different 

Temperatures. 



278° 


4.52 X 10-= 


295° 


1.46 X 10-^ 


323° 


3.26 X 10-'' 


343° 


5.9 X 10' 



It will be observed that, as might be expected, the absolute speed of the 
sodium ion is relatively very low. On the other hand, corresponding to 
the greatly increased conductance of glass with increasing temperature, 
the speed of the sodium ion increases largely with temperature. 

4. Solid Electrolytes. Solid substances, both crystalline and amor- 
phous, conduct the electric current with more or less facility. In the 
case of the insulators, where the conductance is of an extremely low 
order it is not unlikely that conductance is due to the presence of traces 
of impurities. The only substance for which this has actually been 
shown is crystalline quartz, in which the conductance is due to the pres- 
ence of traces of sodium as impurity .^^ jjere the current is carried by 

"Warburg and Tegetmeier, Ann. d. Phya. 35, 455 (1888). 



360 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

the sodium ion which alone is capable of motion in these crystals. The 
process of conduction appears to be entirely similar to that in glasses. 
The typical salts, below their melting point, conduct the current, in 
some cases, with extreme facility. As a rule, the conductance increases 
with increasing temperature according to an exponential curve. The 
specific conductance may be expressed fairly well as a function of tem- 
perature by means of the equation: 



(132) 



log \i = a-{- bt, 



where a and b are constants. In the following table are given values of 
the specific conductance of a few salts at temperatures through their 
melting points.^* 



TABLE CXLIV. 

Conductance of Salts through the Melting Point. 



TlCl 



AgCl 



t 


Jt 


t 


I* 


250° 


0.00005 


250° 


0.00030 


300 


0.00024 


300 


0.0015 


350 


0.0009 


350 


0.0065 


400 


0.0037 


400 


0.026 


427 (M.P.) 


(0.0067 
11.082 


450 
455 


0.11 
M.P. 


450 


1.17 


456 


3.76 


500 


1.332 


500 


3.91 


600 


1.700 


600 


4.16 


AgBr 






Agl 


t 


1^ 


t 


ti 


200° 


0.00052 


125° 


0.00011 


240 


0.0023 


140 


0.00026 


280 
350 


0.0091 
0.08 


144.6 


(0.00034 
U-31 
1.33 


400 


0.38 


150 


419 


0.51 


250 


1.78 


422 


M.P. 


350 


2.14 


425 


2.76 


450 


2.41 


500 


2.92 


550 


2.64 


600 


3.08 


552 


M.P. 






554 


2.36 






600 


2.43 






650 


2.47 



"Tubandt and Lorenz, Ztschr. f. phya. Chem. 87, 513 (1914). 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 361 



iiO 


















> 


^ 


* - 

7^/ 






















y 


/* 


























r 




































































io 






















H""*' 






















w 


^ 
























f 




*^ 


: 
























'y 


1^ 


_-^ 


^ 


%! 




1 

o 

3 












V 


Jr" 






(*-* 


















,/ 


/ 
















'3 








/ 




















03 






/ 


























/ 


























' 


P 
























io 


































































































f 


























^ 


f 
























*tff 


^ 


^ 


i 












% 


^'^^ 


* — 7 


W* 


""iJ 


f 


M 


10* 


61 


lO" 


(f< 


r.o" 


il 


10 



Temperature. 

Fig. 62. Specific Conductance of Silver Halides at Various Temperatures Through 

Their Melting Points. 

The relation between the conductance and the temperature is shown 
graphically in Figure 62. In general, the conductance of the solid salt 
increases with temperature according to Equation 132 up to the melting 



362 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

point, where a discontinuity occurs, a large increase taking place on 
fusion. Silver iodide, however, forms an exception to this rule. This 
substance exhibits a transition point at 144.6°. Below this temperature 
the conductance of silver iodide increases with temperature in a manner 
similar to that of silver chloride and bromide. At the transition point, 
the specific conductance increases from a value of 3.4 x 10'* to 1.31. 
Beyond the transition point, the conductance of silver iodide increases 
slowly with the temperature, the temperature coefficient being not greatly 
different from that of fused salts, as may be seen from the figure. It 
will be observed, furthermore, that at the melting point the conductance 
of solid silver iodide is markedly higher than that of the fused salt, the 
conductance on melting decreasing from 2.64 to 2.36. Even at the tran- 
sition point, at a temperature as low as 144.6, the specific conductance 
of solid silver iodide is of the order of magnitude of that of fused salts. 
This is a remarkable phenomenon and shows that the power of con- 
ducting the current with facility is by no means restricted to the liquid 
state. Thus far, however, silver iodide is the only solid salt whose con- 
ductance in the solid state has been found to be comparable with that 
in the liquid state far below its melting point. 

The conduction process in solid salts of this type is purely electrolytic, 
as follows from the fact that Faraday's Law holds true within the limits 
of experimental error. In the following table are given the observed 
amounts of silver precipitated on electrolysis, together with the amounts 
of silver precipitated in a silver coulometer carrying the same current.^* 

TABLE CXLV. 

Test op Faraday's Law in Solid Electrolytes. 

Ag Ag 

Dissolved Precipitated 
Electrolyte Temperature at Anode in Coulometer % Dif. 

Silver Iodide 540° 0.7212' 0.7139 -1-120 

" " 540 0.5642 0.5623 +0.34 

150 0.7841 0.7804 +0.48 

' " .^ 150 0.7767 0.7706 +0.80 

Silver Bromide 400 0.5883 0.5842 4- 70 

Silver Chloride 430 0.3779 0.3751 -j- 075 

Considering the small amount of silver precipitated or dissolved and 
the difficulty of carrying out the experiments, the agreement between 
the observed and the calculated values of the amount of silver dissolved 

"Tubandt and Lorenz, loo. cit. 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 363 

at the anode is remarkably good. The applicability of Faraday's Law- 
has been further verified by Tubandt and Eggert." There can be little 
question but that, in the case of these salts, Faraday's Law holds true. 

By employing solid silver iodide above its transition point in contact 
with a silver cathode, Tubandt ^^ has found it possible to test Faraday's 
law in the case of other electrolytes than the silver salts and, further- 
more, has been able to carry out transference measurements in order to 
determine to what extent the conductance in solid electrolytes is due to 
the positive and to what extent it is due to the negative carrier. It has 
been shown that for silver iodide, silver bromide, silver chloride, silver 
sulphide, above its transition point, and copper sulphide (Cu^S), Fara- 
day's Law holds and that in these salts the current is carried entirely by 
the positive ion. These results are very significant in that they show 
that one set of ions in these solids forms a fixed framework through which 
the other ions move with considerable facility. In the above salts, the 
negative ions form the framework through which the positive ions move. 
In lead chloride, however, the current is carried by the negative ion; 
the positive ions form the framework through which the negative ions 
move. These facts have an important bearing on the theory of the 
structure of solid salts. 

Silver sulphide has a transition point at 179°. Above the transition 
temperature, as was shown by actual electrolysis of the salt, Faraday's 
Law holds and the current is carried entirely by the positive ions. Below 
the transition temperature, the p form of' silver sulphide appears to con- 
duct in part metallically. In the p form of silver sulphide, Faraday's 
Law does not hold, only about 80 per cent of the current being carried 
by the silver ion. The negative ion in this case is apparently not in- 
volved in the conduction process, the remainder of the current being 
carried by a metallic process of conduction. Apparently, therefore, solid 
electrolytes exist in which the current is carried partly metallically and 
partly electrolytically. As we shall see in a subsequent chapter, solu- 
tions of the alkali metals in liquid ammonia likewise conduct the cur- 
rent by a mixed process. 

The conductance of a heterogeneous mixture of two solid electrolytes 
is approximately a linear function of the composition of the mixture. 
When two solid electrolytes form mixed crystals, however, the conduc- 
tance of the homogeneous mixture is often much greater than that of 
the pure constituents. In the following table are given values of the 

"Tubandt and Eggert, ZtscJtr. J. anorg. Chem. UO, 196 (1920). 
"Tubandt, Ztsch/r. }. Electroch. 26, 358 (1920). 



364 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

specific conductance \i x 10^ of mixtures of sodium chloride and potas- 
sium chloride at 570°." 

TABLE CXLVI. 

Conductance of Mixtures op Sodium and Potassium Chloride at 570°. 

%NaCl 10 20 30 40 SO 60 70 80 90 100 

^XIO" 0.87 8.0 16.5 22.0 24.0 24.0 30.0 34.5 40.0 28.0 4.5 

The conductance value of 0.87 for pure potassium chloride at 570° 
has been calculated from the conductance values at somewhat higher 
temperatures by means of Equation 132. It will be observed that the 
conductance curve exhibits a maximum in the neighborhood of 80 per 
cent of sodium chloride, at which point the conductance of the mixture 
is nearly ten times that of pure sodium chloride and forty times that of 
pure potassium chloride. Apparently, the maximum lies toward the 
side of that component which possesses the higher conductance. Other 
systems of mixed crystals have yielded similar results. Apparently; 
therefore, it is a general rule that the conductance of mixed crystals is 
much greater than that of the pure components. 

In the case of mixtures of silver iodide with silver bromide and with 
silver chloride, the conductance-temperature curve of the resulting mix- 
ture exhibits discontinuities as a result of the peculiar nature of silver 
iodide.^^ Up to 80 per cent of silver bromide, a homogeneous phase re- 
sults initially, whose conductance curve corresponds with that of silver 
iodide above the transition temperature of 146.5°. Apparently then in 
these mixed crystals, the silver bromide is present in a condition similar 
to that of silver iodide above its transition point. The details of the 
conductance curves of these mixtures need not be discussed further here. 
It may be noted, however, that a study of the conductance of various 
solid systems is capable of throwing light on the phase relations in these 
systems. 

It will be evident from the foregoing discussion that solid electrolytes 
exhibit a marked variety of phenomena which have an important bearing 
on our conceptions of the nature of the conduction process, as well as 
upon that of the structure of solid salts. The available data are as yet 
extremely meager, but it may be expected that, as this field is further 
developed, results of great value will be obtained. 

5. Lithium Hydride. The conductance of lithium hydride, both in 
the solid and in the liquid condition, has been investigated by 'Moers.-^' 

"Benrath and Wainoff, Ztschi: 1. phys. Chem. 77 2.57 (mm 
"Tubandt and Lorenz, loc. cit. ' y-^i^^}. 

'"Moers, ZUchr. /. anorg. Chem. lis, 179 (1920). 



PURE SUBSTANCES, FUSED SALTS, SOLID ELECTROLYTES 365 

In the following table are given values of the specific conductance of 
lithium hydride at different temperatures. 

TABLE CXLVII. 

Specific Conductance op Lithium Hydride at Different 
Temperatures. 



t 

443° 

507 

556 

570 

597 

638 



2.124 X 10-= 
2.113 X 10-* 
8.447 X 10-* 
1.491 X 10-* 
3.225 X 10-' 
1.139 X 10-2 



t 

661.5° 
685 
725 
734 

754 



1* 
2.018 X 10-=^ 
3.206 X 10-=' 
7.59f^ X 10"^ 
1.125 X 10-1 
1.01 



The values of the specific conductance may be represented by means 
of a sum of terms in ascending powers of the temperature. It is interest- 
ing to note that the same equation applies both above and below the 
melting point of lithium hydride, which is 680°. Apparently, therefore, 
there is no discontinuity in the conductance of this hydride at its melt- 
ting point. This behavior is exceptional. 

This salt exhibits polarization when a direct current is passed through 
it, and it has been shown that, on the passage of the current, lithium is 
deposited at the cathode and hydrogen evolved at the anode. The cur- 
rent is therefore conducted by either one or both of the ions Li+ and H-. 
This salt, therefore, presents a very interesting case, not only in that the 
conductance of the solid is the same as that of the liquid at its melting 
point, but, also, in that hydrogen appears here as a negative ion. This 
is the only case so far observed in which hydrogen has been shown to 
function in this manner. 

The behavior of hydrogen in lithium hydride is thus very similar to 
that of certain metallic elements in their compounds with the alkali 
metals in liquid ammonia, referred to in a preceding chapter. We saw 
there that, for example, in a solution containing lead and sodium, lead 
is dissolved at the cathode and precipitated at the anode. In the pres- 
ence of very electropositive elements, less electropositive elements tend to 
take up negative electrons and function as anions. This dual function 
of many elements, which ordinarily act as cations, is very significant 
from the standpoint of the constitution of many compounds in which 
these elements are involved. 



Chapter XIV- 

Systems Intermediate Between Metallic and Electrolytic 

Conductors. 

1. Distinctive Properties of Metallic and Electrolytic Conductors. 
Substances which possess the power of conducting the electric current 
are, in the main, sharply divided into two classes; namely, metallic 
and electrolytic conductors. The members of each of these two classes 
of conducting substances have many properties in common with one 
another, which properties serve to distinguish the members of one class 
from those of the other. It is in their optical and electrical properties 
that the members of the two classes exhibit the greatest contrast. While 
electrolytic systems, in general, are transparent, metallic systems are 
non-transparent and exhibit metallic reflection. Electrolytic systems 
conduct the current with the accompaniment of material effects, while 
metallic systems conduct the current without attendant material effects 
of any kind. Nevertheless, the view has been gradually gaining ground 
that the conduction process in the two systems is similar in that conduc- 
tion is effected by the motion of charged particles. While we possess a 
more or less comprehensive theory of the mechanism whereby the transfer 
of the charge is affected in electrolytic systems, a similar theory does 
not exist for metallic systems. Such knowledge as we do possess regard- 
ing the existence of charged particles in metals is founded chiefly on 
observations on the properties of metals other than those relating imme- 
diately to the conduction process. There exists little direct evidence 
showing that the passage of the current through the metals is effected 
by the motion of charged particles. 

The great difficulty in the way of a direct attack on the problem of 
metallic conduction lies in the absence of material effects accompanying 
the passage of the current. In addition, there has been a complete lack 
of systems exhibiting properties intermediate between those of metallic 
and electrolytic conductors. Conducting systems fall sharply into 
one of two classes; namely, metallic and electrolytic conductors. In 
recent years, however, a class of solutions has been subjected to investi- 
gation which appears to bridge the gap between metallic 9,nd electrolytic 
conductors; in other words, which exhibits properties, on the one hand in 

366 ' 



SYSTEMS INTERMEDIATE 367 

common with those of metallic systems and, on the other hand, with 
those of electrolytic systems.^ These are solutions of the alkali metala 
and the metals of the alkaline earth in liquid ammonia and organic 
derivatives of ammonia. In order to make clear the bearing of these 
solutions on the problem of metallic conduction, it will be necessary to 
discuss in some detail the properties of these solutions of the metals in 
liquid ammonia. 

2. Nature of the Solutions of the Metals in Ammonia. The alkali 
metals are extremely soluble in liquid ammonia, yielding solutions whose 
external appearance depends upon their concentration. Dilute solutions 
of the alkali metals, as well as of metals of the alkaline earths, exhibit a 
fine blue color, whose absorption for all wave lengths is relatively 
great.^* At higher concentrations, the solutions possess a marked re- 
flecting power for all wave lengths. Very concentrated solutions exhibit 
distinct metallic reflection of a color intermediate between that of copper 
and gold. Among the earlier investigators of these solutions there was 
much discussion as to whether the metal exists in solution as such or as 
a compound with the solvent. Cady ^ showed that these solutions are 
excellent conductors of the electric current and that in concentrated 
solutions the passage of the current is characterized by the absence of 
polarization effects at the electrodes. Finally, it has been shown that, 
in the case of the alkali metals, stable compounds between the metals 
and the solvent cannot be separated from these solutions.^ While com- 
pounds between the metal and the solvent may exist in solution, such 
compounds, if they exist, possess little stability as follows from the low 
value of the energy changes accompanying the process of solution. In 
the case of the metals of the alkaline earths, however, it has been shown 
that compounds may be separated from solution, in which the metal is 
combined with ammonia. Kraus has prepared the compound Ca(NH3)„ 
and recently Biltz * has prepared the compounds BalNHa)^ and 
Sr(NH3)6. These compounds possess a metallic appearance, resembling 
that of the concentrated solutions of the metals in ammonia. 

Kraus has determined the vapor pressure of solutions of sodium in 
liquid ammonia, from which he calculated the molecular weight of the 
metal in these solutions. Since the molecular weight can be determined 
only in dilute solutions, where the properties of the system are approach- 
ing those of an ideal system, it follows that molecular weight determina- 

> Kraus, J. Am. Ghem. Soc. m, 1557 (1907) ; iUd., SO, 653, 1157 and 1323 (1908) ; 
ibid., Se, 864 (1914) ; ibU., iS, 749 (1921). 

"Gibson and Argo, J. Am. Ghem. Soc. iO, 1327 (1918). 
2 Cady, J. Phys. Chem. 1, 707 (1897). 
•Kraus, J. Am. Ohem. Soc. SO, 653 (1908). 
♦ BiJtz, Ztachr. f. Electroch. ««, 374 (1980), 



368 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tions are always more or less in doubt. However, if the molecular weights 
are determined at a series of concentrations, it is possible to draw an 
inference as to the limit approached, as the concentration of the solution 
decreases, from the manner in which the apparent molecular weight 
varies as a function of the concentration. In the following table are 
given values of the apparent molecular weight of sodium dissolved in 
liquid ammonia at different concentrations, and in Figure 63 are shown 
these values plotted as ordinates against the logarithms of the concen- 
trations as abscissas. 

TABLE CXLVIII. 

Apparent Moleculae Weight of Sodium in Ammonia at 
Different Concentrations. 

C Apparent Mol. Wt. C Apparent Mol. Wt. 

2.903 32.23 0.3665 25.31 

1.841 30.70 0.3587 25.27 

1.220 29.06 0.2669 23.53 

0.9910 28.80 0.2516 23.43 

0.9038 28.46 0.2261 23.41 

0.5614 26.39 0.1565 21.62 

0.5558 26.47 0.1519 21.58 

0.4104 25.36 

It will be seen that, as the concentration decreases, the calculated value 
of the molecular weight decreases very nearly as a linear function of 
the logarithm of the concentration over the ranges of concentration 
investigated. It is not possible to state what value the molecular weight 
approaches as a limit, but it is evident that the limit approached has a 
value less than 23, the atomic weight of sodium. It appears, therefore, 
that sodium dissolved in liquid ammonia exists in an atomic condition 
and it is probable that the limit, which the molecular weight approaches, 
has a value less than the atomic weight of sodium. This indicates the 
presence of a molecular species other than the sodium atom in these 
solutions. While similar molecular weight determinations have not been 
carried out in solutions of metals other than sodium, nevertheless, in 
view of the similarity of the properties of solutions of the different metals 
in ammonia, it is highly probable that the state of these metals differs 
little from that of sodium. 

3. Material Effects Accompanying the Current. The criterion for 
determining whether a given substance is a metallic or an electrolytic 
conductor is the absence or existence of material effects accompanying 
the passage of the current. In dilute solutions of the metals in liquid 



SYSTEMS INTERMEDIATE 



369 



ammonia, it has been definitely established that material effects accom- 
pany the current through these solutions. The existence of such effects 
IS readily observed as a consequence of the characteristic color of these 
solutions. If a current is passed between two platinum electrodes in 
dilute solution of sodium or potassium in liquid ammonia, it is found 
that the color in the immediate neighborhood of the cathode is intensi- 
fied. This result is obviously due to the fact that, as the current passes 
through the solution, the metallic element as an ion, either simple or 
complex, is carried up to the cathode. The electrolytic character of the 




/.9 0.0 0.1 e.a o,3 o.t o.s o.e on o.g o.a l.o i.i i.z 1.3 

Log V. 

Fig. 63. Apparent Molecular Weight -«f Sodium in Liquid Ammonia at Different 

Concentrations. 



conduction process in dilute solutions of these metals in liquid ammonia 
is therefore established; the metal is associated with the positive ion. 
Taking into consideration the great tendency of the alkali metals to 
act as positive ions, it is probable that in these solutions the metals are 
present, in part at least, as charged atoms which do not differ from the 
positive ions of salts of the same metals dissolved in the same solvent. 
If positive ions are present in these solutions, then, obviously, nega- 
tive ions must be present likewise. So far as may be observed, when a 
current passes through a solution of a metal dissolved in liquid ammonia, 
no material effect occurs at the anode, save that the concentration of 
the metal in the immediate neighborhood of this electrode is diminished. 



370 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

In dilute solutions, this effect is very pronounced and, in the immediate 
neighborhood of the anode, the solvent appears to be completely freed 
from the metal, since the solution becomes colorless and transparent. 
No reaction of any kind appears to take place at the anode surface, no 
gas is evolved, nor is any manner of deposit observable. On subjecting 
a solution of sodium in ammonia contained in a U-shaped tube to ex- 
tended electrolysis, the metal may be completely removed from the 
anode limb and transferred to the immediate neighborhood of the 
cathode surface. In this, no actual loss of the metal occurs, since on 
reversing the current, or on mixing the solution by shaking, the original 
solution is reproduced. Apparently, therefore, there is present in these 
solutions a negative carrier whose passage into the anode leaves behind 
it no observable material effect. The nature of the phenomenon is not 
appreciably altered if another metal is employed in place of sodium. 
We commonly associate the characteristic metallic properties of a 
substance with the atoms of this substance; and, in the case of com- 
pounds, we associate metallic properties with the electropositive con- 
stituent. A brief consideration, however, will serve to show that this 
conception is erroneous, and that the electropositive constituent of a 
compound is entirely nonmetallic in its character. The metals owe their 
characteristic metallic properties, not to the electropositive constituent 
present, but, rather, to a common electronegative constituent. If a solu- 
tion of potassium in liquid anunonia, which has a characteristic color, 
is placed between two solutions of potassium amide, which are trans- 
parent, then, on passing a current through this system of solutions, the 
motion of the color indicates the direction in which the free metal is 
transported under the action of the current. If the characteristic prop- 
erties of a solution of potassium in ammonia were due primarily to the 
presence of an electropositive coiistituent, then we should expect that 
the color would move toward the cathode. It has been found, however, 
that, actually, under these conditions, the color moves toward the anode. 
As has been shown, potassium in liquid ammonia solutions is associated 
with the cation and moves toward the cathode. It follows that the 
transfer of the free metal in the solution, placed between the two solu- 
tions of potassium amide, is effected by means of the negative carrier. 
In passing a current through a system of the type described above, there 
is no indication that anything takes place as the positive ions pass from 
the potassium solution into the solution of potassium amide, save that 
the color boundary gradually moves in a direction opposite to that of 
the positive current, that is, toward the anode. It is probable, there- 
fore, that the positive Ion in a solution of metallic potassium in liquid 



SYSTEMS INTERMEDIATE 37I 

ammonia is identical with the positive ion of a solution of potassium 
amide in this solvent. In other words, there is present in a solution of 
metallic potassium a positive carrier identical with the positive carrier 
in potassium amide. 

The positive carrier, then, in a solution of a metal in liquid ammonia, 
is nothing other than the normal ion of this metal and its properties in 
the metal solution differ in no wise from its properties in a solution of 
its salts. On the other hand, it is evident that, as the negative carrier 
moves toward the anode from the potassium solution to the potassium 
amide solution, free metallic potassium, that is, metallic potassium not 
chemically combined, is carried in the direction of the negative current 
toward the anode. The metallic properties of the solutions of the alkali 
metals in ammonia, therefore, must be due, primarily, to the negative 
carrier, and since free metallic potassium is present in that portion of 
the solution where blue color is present, it follows that this metal is 
generated by interaction between the potassium ion of the potassium 
amide solution and the negative carrier present in the solution of metallic 
potassium which, under the action of the potential gradient, moves into 
the potassium amide solution. This negative carrier, which in all like- 
lihood is identical with the negative electron, is the essential metallic 
constituent of metallic substances. 

There evidently exists in a metal solution an equilibrium of the type 

M* + e- = Me, 

where M+ is the metallic ion, e" is the negative ion (negative electron) 
and Me is the neutral metallic atom. In the amide solution, as is well 
known, there exists an equilibrium according to the equation: 

M^ + NH^- = MNH^. 

It is evident that, as the negative carrier e" is carried into the metal 
amide solution, equilibrium establishes itself between this carrier and the 
other molecular species present. In other words, the reaction takes place: 

M+ + e- = Me. 

The total amount of free metal in the solution at any time is e- + Me. 
To what extent the metal atoms are ionized into normal positive ions 
and negative electrons will appear below. 

4. The Relative Speed of the Carriers in Metal Solutions. If the 
conduction process in metals consists essentially in a transfer of charge 
due to the motion of the negative carriers, since no material effects are 
observable at the boundaries between different metallic conductors, it 



372 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

follows that the negative carrier in all metals is the same. If this is 
true, and if the negative carrier in the solutions of the alkali metals in 
ammonia is the negative electron, then those properties of these solu- 
tions which depend upon the negative carrier should be the same in 
solutions of different metals. In how far this is true we shall see pres- 
ently, since many of the properties of these solutions have been analyzed 
in terms of their ionic constituents. 

Since the solutions of the metals in ammonia are ionized, the prob- 
lem of determining the nature of the conduction process may be attacked 
in a manner similar to that employed in the case of ordinary electrolytic 
solutions. It, is possible, in the first place, to determine the relative 
amount of the current carried by the two ions under given conditions. 
For this purpose, transference measurements might be carried out, the 
concentration changes resulting when a given quantity of electricity 
passes through the solution being determined. This experiment is diffi- 
cult of execution, and consequently recourse has been had to another 
method, the results of which, although they are not as conclusive as 
direct transference determinations, nevertheless make it possible to 
determine the general order of magnitude of the quantities involved. The 
electromotive force of a concentration cell with liquid junction is given 
by the equation: 

from which the value of n, the transference number, may be determined, 
if the electromotive force E and the concentrations CiYi and C^y^ are 
known and if the laws of dilute solutions are applicable. Judging by the 
results obtained in solutions of ordinary electrolytes, this equation yields 
results which are approximately correct. In the case of a concentration 
cell which consists of two platinum electrodes placed in metal solutions, 
having concentrations C^ and €^, the work is due to the transfer of n 
mols of sodium per equivalent of electricity from the concentration C^ 
to the lower concentration C^. The cell is similar to that of a salt solu- 
tion with reversible anodes, n is obviously the fraction of the current 
transported by the positive carrier in the solutions. 

In Table CXLIX are given values of the electromotive force of con- 
centration cells at different concentrations— the ratio of the concentra- 
tions of the two solutions was approximately 1:2— together with the 

transference number n of the cation and the ratio ^~'" - 

n 



SYSTEMS INTERMEDIATE 373 

TABLE CXLIX. 



E.M.F. OF Concentration Cells and Values of n and ^ " 



n 
Solutions of Na in NH,. 



FOB 



n 



0.00359 


277.6 


0.0109 


90.6 


0.0231 


41.2 


0.0291 


33.4 


0.0336 


28.8 


0.0385 


25.0 


0.0575 


16.4 


0.0704 


13.2 


0.0980 


9.2 


0.125 


7.0 


. 1—n 
10 : 


in other words, the 



Ca EX lO'' 

0.870 0.080 

0.732 0.328 

0.335 0.620 

0.164 0.72 

0.081 0.86 

0.040 1.07 

0.020 1.38 

0.010 1.80 

0.005 2.60 

0.0024 3.40 



In Figure 64 are shown values of the ratio 

n 

ratio of the charge transported by the negative carrier to that transported 
by the positive carrier. On examining the table, it will be seen that, for a 
given concentration ratio, the electromotive force increases as the con- 
centration decreases. At higher concentrations, the electromotive force 
decreases very rapidly with increasing concentration and ultimately be- 
comes extremely small. Referring to the figure, it is seen that at low 
concentrations the ratio of the carrying capacities of the two ions ap- 
proaches a limiting value; that of the negative carrier being approxi- 
mately seven times that of the positive carrier. As the concentration 
increases, the relative amount of current carried by the negative carrier 
increases, at first slowly and then more and more rapidly. In the neigh- 
borhood of normal concentration, the current carried by the negative 
carrier is several hundred times as great as that carried by the positive 
carrier. As we have seen, the positive carrier in a sodium solution is in 
all likelihood identical with the positive ion of a sodium salt. As Frank- 
lin and Cady have shown, the speed of this ion varies only little with 
concentration. The increased carrying capacity of the negative ion at 
higher concentrations must, then, be due to an increase in the mean 
speed of the negative carriers. 

It is a noteworthy fact that the carrying capacity of the negative 
carrier in dilute solutions is much greater than that of the sodium ion. 
The speed of the negative carriers in these solutions must therefore be 
much greater than that of the sodium ion. The speeds of the different 



374 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



ions of salts in ammonia solution, as we have seen, do not differ greatly. 
This indicates that the negative carrier in the metal solutions is of rela- 
tively small dimensions. Nevertheless, if the negative carrier in these 
solutions were the negative electron unassociated with matter, we should 
expect a much greater value. It is known, however, that, owing to elec- 
trostatic action, a charge placed in a fluid medium tends to condense 
about it an atmosphere of the surrounding molecules. In gases at higher 
pressures, the speed of the negative carrier is as low as, and often lower 



sao 



zso 



200 



ISO 




100 



3.0 



Fig. 64. Relative Speed of the Negative and Positive Ions of Sodium in Liquid 
Ammonia at Different Concentrations. 

than, that of the positive carrier and it is only at low pressures that the 
negative carrier in gases loses its envelope of surrounding molecules 
and acquires a high speed. It is not surprising, therefore, that the nega- 
tive electron in liquid ammonia should possess a speed comparable with 
that of ordinary ions. At higher concentrations, however, as is indicated 
by the increased carrying capacity of the negative ion, the size of the 
surrounding envelope evidently diminishes and, indeed, it has been shown 
that some of the negative carriers are completely unassociated with 
ammonia. 

If the negative carriers are associated with ammonia, then obviously, 



SYSTEMS INTERMEDIATE 375 

due to the motion of this carrier, ammonia will be carried from the 
dilute to the concentrated solution. If the vapor pressures of the two 
solutions are known, we may calculate the work due to the transfer 
of solvent by the negative carrier, the number of molecules of ammonia 
associated with this carrier being assumed. The complete expression 
for the electromotive force is: 

^ = — p- log j^ + m (1 - n) -^ log g-, 

where m is the number of molecules of ammonia associated with the 
negative carrier and p^ and p^ are the vapor pressures of the two solu- 
tions. If we place n = in this equation, that is, if we assume that 
all the current is carried by the negative carriers, we may calculate a 
maximum value for m, if the electromotive force of the cell and the 
vapor pressures of the solutions are known. For a concentration cell 
between solutions whose concentrations were 1.014 and 0.627 normal, the 
measured electromotive force was 0.08 X 10"^ volts, and the ratio of the 
vapor pressures was 1/1.006. This yields for m the value 0.67; that is, 
a value less than unity. Since m cannot be less than unity, it follows 
that at least a portion of the current must be carried by carriers not 
associated with ammonia. It is evident, from the manner in which the 
electromotive force and the vapor pressure of anomonia solutions vary 
with the concentration, that at higher concentrations the value calculated 
for m would be even smaller. The negative carriers in solution, there- 
fore, consist of negative electrons surrounded with ammonia molecules. 
As the concentration of the solution increases, the number of ammonia 
molecules associated with the carriers decreases and ultimately a por- 
tion of the carriers becomes entirely free from ammonia molecules. The 
great increase in the relative carrying capacity of the negative carriers 
at higher concentrations is due to the presence of these free negative 
electrons. 

5. Conductance of Metal Solutions. If the increased carrying 
capacity of the negative carrier is, in fact, due to an increase in the 
mean speed of this carrier, the speed of the positi^'e carrier remaining 
substantially constant, then the equivalent conductance of solutions of 
the metals in liquid ammonia should increase largely with the concentra- 
tion at higher concentrations. Since the determinations of the molecular 
weight, as well as the results on the motion of the' boundary between a 
metal and a metal amide solution, indicate that an equilibrium exists 
between the positive ions and the negative carriers and the neutral 
atoms, it is to be expected that the ionization of the metal will vary as a 



376 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

function of the concentration. According to these views the state of a 
metal dissolved in ammonia does not differ materially from that of a 
salt of the same metal dissolved in this solvent. The only material dif- 
ference lies in the fact that, whereas in the metal solution the negative 
electron functions as negative carrier, in the salt solution, a negative 
ion, that is, a negative electron attached to an atomic complex, serves 
as negative carrier. We should therefore expect the equivalent con- 
ductance in dilute solutions to vary as a function of the concentration 
in a manner similar to that of normal electrolytes. In other words, with 
decreasing concentration of the solution, the equivalent conductance 
should increase and approach a limiting value. 

In Table CL are given values of the equivalent conductance of solu- 
tions of sodium in liquid ammonia at its boiling point at different con- 
centrations. The density of the solutions not being known, the dilu- 
tions given under the column headed V represent the number of liters of 
pure ammonia of density 0.674, in which one atom of sodium is dis- 
solved. In the more concentrated solutions the density is considerably 
lower than that of pure ammonia. 

TABLE CL. 
Conductance of Sodium in Ammonia at — 33.5°.^ 



V 


A 


V 


A 


0.5047 


82490. 


13.86 


478.3 


0.6005 


44100. 


30.40 


478.5 


0.6941 


23350. 


65.60 


540.3 


0.7861 


12350. 


146.0 


650.3 


0.8778 


7224. 


318.6 


773.4 


0.9570 


4700. 


690.1 


869.4 


1.038 


3228. 


1551.0 


956.6 


1.239 


2017. 


3479.0 


988.6 


2.798 


749.4 


7651.0 


1009.0 


6.305 


554.7 


17260.0 


1016.0 






37880.0 


1034.0 



In Figure 65 the upper curve represents . the equivalent conductance as 
a function of log F up to a concentration of approximately normal. From 
an inspection of the table and the accompanying figure, it will be seen 
that the conductance curve exhibits a minimum in the neighborhood of 
0.05 N. At lower concentrations the equivalent conductance increases 
as the concentration decreases and approaches a limiting value in the 
neighborhood of 1016. The form of the curve at these concentrations is 

■Kraus, loo. cit. 



HYSTEMS INTERMEDIATE 



377 



similar to that of binary electrolytes in liquid ammonia, the only ma- 
terial difference being that the conductance has a much higher value. 
The equivalent conductance of the sodium ion is 130. It follows, then, 
that the equivalent conductance of the negative carrier in these solutions 
at low concentrations is in the neighborhood of 886, or 6.8 times that of 
the sodium ion. We saw in the previous section that the results of 
measurements of the electromotive force of concentration cells indicate 
that the carrying capacity of the negative carrier is approximately 7 
times that of the positive ion in a sodium solution. This value, therefore, 
is in excellent agreement with the value 6.8 obtained from conductance 



Fia. 65. 



'3 

D* 





1 












































\ 










A 


^ 


■1-. + 


• : 
+ 


1 


1 


^ 


\ 






/ 












V 


s^ 


V 


^^ 


^ 








* 4^ 







IZOO 

t 

1000 Q 



P. 

BOO 5; 

t3 



t.S 0.0 O.S I.O I.S X.O e.S 3.0 S.S *.0 AJ- 

Log V. 

Equivalent Conductance of Sodium in Liquid Ammonia at — 33.5° at 
Different Concentrations. 



measurements. Evidence has already been presented which indicates 
that the positive ion in a sodium solution is identical with the positive 
ion in a solution of a sodium salt. The fact that the conductance of the 
positive ion, as derived from measurements with the metal solutions, 
corresponds with that of the sodium ion as derived from measurements 
with solutions of sodium salts confirms this hypothesis. The positive 
ion in a solution of sodium in liquid ammonia is therefore the normal 
sodium ion. 

If, now, we examine the conductance curve in the more concentrated 
solutions, we see that below a concentration of 0.05 N the conductance 
increases with the concentration, the increase being the greater the 
higher the concentration. This, again, confirms the conclusion derived 
from a study of the electrorriotive force of concentration cells. As the 
concentration increases, the relative carrying capacity of the negative 
carrier increases. The increase in conductance is due to an increase in 
the mean speed of this carrier, since at higher concentrations the con- 



378 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

ductance increases enormously, which result may be accounted for only 
on the assumption that the speed of one or both of the carriers increases. 
Since one of these carriers is the normal sodium ion, it follows that the 
conductance is due to an increase in the speed of the negative carrier. 
If these conclusions are valid, then, at high concentrations, the conduc- 
tance of the metal solutions should approach that of the metals them- 
selves, for at high concentrations the number of carriers and negative 
electrons present in the solution becomes comparable with that of the 
total number of molecules present, in which case we should expect that 
a considerable fraction of these carriers would be free from ammonia 
molecules. This is borne out by the results of conductance measure- 
ments. As may be seen from Table CL, the equivalent conductance in- 
creases from a value of approximately 475 at a concentration of 0.05 N 
to a value of approximately 2000 at normal and to approximately 82000 
at a concentration of 2 normal. At this concentration the specific con- 
ductance of the solution is 163.5, the specific conductance of mercury 
being 1.063X10*, which is about sixUimes that of the metal solution at 
the concentration in question. The lower curve in Figure 65 shows how 
the conductance varies with concentration up to 2 N. 

In the following table are given values of the specific conductance of 
solutions of sodium in liquid ammonia up to the saturation point of these 
solutions.* 

TABLE CLI. 

Specific Conductance of Concentrated Solutions of Sodium 
IN Ammonia at — 33.5°. 



V 


1^ 


V 


(i 


0.1081 


5047.0 


0.5099 


148.3 


0.1331 


4954.0 


0.7612 


20.21 


0.1804 


2687.0 


0.9265 


5.988 


0.2768 


1070.0 


1.298 


1.269 


0.3230 


714.0 


1.674 


0.6465 



The results for sodium, together with those for potassium, are shown 
graphically in Figure 66, where the logarithms of the specific conduc- 
tance are plotted against the logarithms of the dilution V as defined 
above. The curve passing through the points is that of potassium; the 
other, that of sodium. At the highest concentrations, the solutions were 
saturated, so that the specific conductance was independent of the total 
amount of ammonia present. The second point for the value V = 0.1331 

•Kraus and Lucasse, J. Am. Chem. Soc. iS (Dec, 1921). 



SYSTEMS INTERMEDIATE 379 

lies just below the saturation point. The specific conductance of the 
saturated solution is 0.5047 X 10^ or, almost precisely one half that of 
mercury at 0°. That the solutions of the metals in liquid ammonia at 
these concentrations are metallic admits of no doubt. They exhibit all 
the properties of metallic substances, both optical and electrical. A 
brief consideration will show, indeed, that in these solutions the metal 
possesses an exceptionally high conducting power compared with that of 




Fia. 66. Conductance of Concentrated Solutions of Sodium and Potassium in 

Liquid Ammonia at — 33.5°. 



many metals. Obviously, if metallic conduction is due to the motion of 
charged carriers, then two factors influence the conductance; in the first 
place, the resistance which the carriers experience in their motion, and, 
in the second, the number of carriers present in a given volume. In 
comparing the conducting power of different metals, it is not sufficient 
to merely compare their specific conductances. The concentration factor 
should also be taken into account. If the specific conductance is divided 
by the number of gram atoms per cubic centimeter, the ratio yields the 
atomic conductance of the metal. The atomic conductance of a satu- 



380 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 



rated solution of sodium in ammonia «* is 1.1 X 10' The atomic con- 
ductance of metallic sodium at room temperatures is 5.05 X 10'- The 
conductance of the saturated solution is therefore comparable with that 
of the pure metal. Values of, the atomic conductance of other metals will 
be found in Table CLIII of the next chapter. The atomic conductance of 
sodium solutions is about the same as that of osmium and tin and much 
greater than that of mercury (liquid) and bismuth. 
/f-oo 



1300 



IZOO 




Fig. 67. 



Conductance of Dilute Solutions of Potassium and Lithium and of Mix- 
tures of Sodium and Potassium in Liquid Ammonia at — 33.5°. 



The view was expressed, above, that the negative carrier for dif- 
ferent metals dissolved in liquid ammonia is the same and is, in fact, the 
negative electron, which carrier presumably effects the passage of the 
current through all metallic substances. If this view is correct, then, at 
higher concentrations, where the conductance of the solution is due 
almost entirely to the negative electron, solutions of different metals in 
ammonia should exhibit very nearly the same properties. It is to be 

"»ThIa Is based on tbe value 0.54 for the density of the saturated solution as deter- 
mined approximately by Dr. Lucasse In the Author's Laboratory. This value may be in 
error by several per cent. 



SYSTEMS INTERMEDIATE 381 

expected, of course, that minor variations will be observed, since equiva- 
lent solutions are not physically identical. The densities of potassium 
and sodium solutions, for example, differ; and the amount of ammonia 
associated with the positive ions in these solutions doubtless differs. 
Aside from minor differences, we should expect those properties of metal 
solutions, which depend upon the negative carrier, to be relatively inde- 
pendent of the nature of the metal. In Figure 67 are shown the conduc- 
tance curves of dilute solutions of potassium, lithium, and mixtures of 
sodium and potassium. The uppermost curve is that of potassium, the 
lowest that of lithium, while the intermediate curve is that of a mixture 
of sodium and potassium. The curve for mixtures of sodium and potas- 
sium lies intermediate between that of sodium and of potassium. It is 
seen that in the case of very dilute solutions of potassium and lithium, 
the conductance values, as shown, lie below the true values owing to the 
fact that these metals react with the solvent according to the equation: 

Me 4- NH3 = MeNH^ + iH,; 

that is, the metals react with the solvent to form the amides. This re- 
moves a portion of the metal from solution and consequently the con- 
ductance values measured are lower than the true values. From the 
extensive data presented by Kraus, however, there can be no doubt as 
to the cause for the low values observed in dilute solutions in the case 
of potassium and lithium. At intermediate concentrations, where the 
formation of amide is not marked, the conductance of the solutions 
diminishes in the order: potassium, sodium, lithium. At a given con- 
centration, the difference in the_ values of the conductance of these 
metals corresponds approximately to the difference in the conductance 
of the positive ions of these metals. This shows that in dilute solutions 
of potassium, sodium and lithium in liquid ammonia, the conductance of 
the negative carrier is the same; presumably, therefore, the negative car- 
riers are identical in the three cases. At higher concentrations, where 
the conductance of the positive ion becomes negligible in comparison 
with that of the negative carrier, we should expect the specific conduc- 
tance of the solutions to be practically the same at the same equivalent 
concentration. As may be seen from Figure 66, the conductance curves 
for sodium and potassium possess the same form, and over a considerable 
range of concentration they are practically identical.' At higher con- 
centrations, slight variations occur as might be expected, since the den- 
sities of these solutions are not the same. The conclusion that the 

' Kraus and Lucasse, loc. cit. 



382 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

negative carrier of the different metals is the same appears, therefore, 
amply justified. 

The temperature coeflBcient of sodium solutions in liquid ammonia 
has been measured. In Table CLII are given values of the resistance 
of fairly dilute sodium solutions from the boiling point of liquid ammonia 
up to 85°C. In the last column are given values of the mean percentage 
temperature coefficient of these solutions over various temperature inter- 
vals referred to the resistance at — 33°.^* 

TABLE CLII. 

Temperatuee Coefficient of Dilute Sodium Solutions. 

JMV^ X 100 



t 


Xl/ 


MH/R},, ^ 


— 33° 


124.3 


, , 


— 13° 


85.7 


2.25 


+ 17° 


43.4 


4.69 


+ 48° 


28.2 


5.34 


+ 85° 


15.6 


9.00 



It is seen that at low temperatures the temperature coefficient of the 
conductance of these solutions is approximately 2 per cent, and as the 
temperature increases the temperature coefficient increases markedly 
reaching a value of 9 per cent for the interval between 45° and 85°. 
This behavior of the metal solutions in liquid ammonia is in striking 
contrast to that of normal electrolytes dissolved in this solvent. At 
ordinary concentrations, the conductance of these solutions passes 
through a maximum in the neighborhood of room temperatures, the 
conductance decreasing with increasing temperatures above this point. 
It is obvious that the factors involved in the temperature coefficients of 
the metal solutions are very different from those involved in solutions of 
ordinary electrolytes. It is difficult, in the present state of our knowl- 
edge, to state to what the high value of the temperature coefficient is 
due. However, since in fairly dilute solutions the conductance is due 
primarily to the negative electron more or less associated with ammonia, 
it is possible that the high value of the temperature coefficient at higher 
temperatures is due to an increase in the mean speed of the negative 
carriers as a result of a diminution in the size of the solvent envelope 
with which the negative electrons are surrounded. 

While at low concentrations the temperature coefficient of the metal 

'• Kraus, Joe. cit. 



SYSTEMS INTERMEDIATE . 383 

solutions is greater than that of ordinary electrolytes, at high concen- 
trations the temperature coefficient is markedly lower.' At a dilution 
V = 0.18, the temperature coefficient is approximately 0.17%. It is 
evident that at higher concentrations the value of the temperature coef- 
ficient decreases as the concentration increases. In the neighborhood of 
the saturation point, the coefficient is not far from zero, and, were it 
possible to prepare solutions having higher concentrations, it might be 
expected that the temperature coefficient would even become negative 
as it is in metals.** 

These data on the temperature coefficient of the metal solutions in 
liquid ammonia serve further to differentiate these solutions from solu- 
tions of ordinary electrolytes. The behavior of the very concentrated 
solutions clearly indicates an intimate relation between these solutions 
and ordinary metallic conductors. The properties of the metal solutions 
in liquid ammonia, therefore, supply abundant evidence to the effect 
that conduction in metals is due to the motion of a negative carrier of 
sub-atomic dimensions, which carrier is the same for all metals. Since 
the only carrier of sub-atomic dimensions which has been observed is the 
negative electron, we may infer that the effective carrier in metals, as 
in these solutions, is the negative electron. 

' Observations by Dr. W. W. Lucasse In the Author's Laboratory. 

»» Since tliis was written, the temperature coefficient of sodium in liquid ammonia 
has been determined by Dr. Lucasse from a dilution 7 = 1.7 up to the saturation point. 
The coefficient for the saturated solution is 0.067%. As the concentration decreases, the 
temperature coefficient increases decidedly reaching a maximum of 3.65% at F^1.06 
after which it decreases more slowly, falling to 2.47% at F = 1.7. 



Chapter XV. 
The Properties of Metallic Substances. 

1. The Metallic State. With the exception of the elements of the 
argon group and the strongly electronegative elements of lower atomic 
weight, elementary substances are metallic. Compounds between 
strongly electronegative and strongly electropositive elements, as well 
as compounds between the more electronegative elements, are non- 
metallic; while compounds between distinctly metallic elements are 
throughout metallic. Compounds between the less strongly electronega- 
tive elements and the less strongly electropositive elements are often 
metallic in the solid state. Thus the compounds of the alkali metals 
and the metals of the alkaline earths with the elements of the halogen 
and of the oxygen groups are non-metallic ; while compoimds of the less 
electropositive elements, such as lead and iron, with the elements of the 
oxygen group are often metallic. Within this class are also included 
certain free electropositive groups, containing both metallic and non- 
metallic elements, and possibly groups containing only nonmetallic 
elements. Thus, the free group CHgHg is metallic,^ while certain of 
the substituted ammonium groups form stable metallic amalgams.i^ 
There is also evidence that the quaternary substituted ammonium groups 
are soluble in ammonia in the free state, and that in solution their prop- 
erties resemble those of the alkali metals.^ The property of metallicity, 
therefore, is not to be looked upon as an atomic property, since various 
groups of nonmetallic elements in the free state exhibit metallic 
properties. 

The metals thus comprise a major portion of the elementary sub- 
stances and a large number of compounds between metallic and non- 
metallic elements. While nonmetallic compounds may, in a large 
measure, be accounted for through the interaction of the negative elec- 
trons with atoms, a similar theory of the constitution of metallic com- 
pounds has not thus far been developed. One of the remarkable facts 

>KrauB, J. Am. Ohem. Soe. SS, 1732 (1913) 
'McCoy and Moore, J. Am. Chem. 8oc. SS, 273 (1911) 
■ Palmaer, Ztgphr. f. Mlehtroch. 8, 729 (1902) ; Kraus, loo. cit 

384 



THE PROPERTIES OF METALLIC SUBSTANCES 385 

in connection with inter-metallic compounds is the large number of 
compounds derivable from a single pair of elementary substances. The 
constitution of these compounds does not harmonize well with our pres- 
ent conceptions of valence. The study of these substances is attended 
with many experimental difficulties and their nature at the present time 
is little understood. 

Metallic substances are characterized by certain well-defined prop- 
erties, chiefly electrical and optical, which are common to all.* This 
community of property among metallic substances indicates some com- 
mon element within their constitution. During the past few decades the 
view has been gaining ground that the properties of metallic substances 
are primarily due to the presence of charged particles, presumably nega- 
tive electrons, which are relatively free to move within the body of the 
metal. While this theory of the constitution of metals is in good agree- 
ment with observed facts from a qualitative point of view, it has not 
been found possible to elaborate a detailed theory of metallic substances 
which accounts successfully for the major portion of their characteristic 
properties. 

2. The Conduction Process in Metals. Metallic conductors are dif- 
ferentiated from electrolytic conductors in that the passage of the cur- 
rent through them is unaccompanied by an appreciable transfer of mat- 
ter. If a current is passed for an indefinite period of time through a 
series of metallic conductors, no material effects are observable, either 
within the conductors themselves or at the boundaries between them. 
If the conduction process in metals is due to the motion of negative 
electrons; then there must likewise be present in the metals positively 
charged constituents or ions which, conceivably, may take part in the 
conduction process. In all likelihood the amount of matter transferred 
by these carriers is extremely small, and may under ordinary conditions 
escape observation. Experiments carried out with amalgams of sodium 
and potassium indicate that in these systems an appreciable transfer of 
matter actually takes place.^ Curiously enough, in these amalgams, the 
electropositive constituent, that is, the alkali metal, was found to be 
carried toward the anode and not toward the cathode as might have 
been expected. The data are as yet too meager to warrant drawing 

» A verr complete summary of the literature relating to metallic substances is given 
bv T KoSgsbeFger in Handbuch d. Blektrizitat u. d. Magnetismus by L. Graetz, Leipzig, 
Y A Rifrthf 1920) Vol S, pp. 597-724. The older literature is also summarized in 
Vfnketaann'i Handbuch d'. Physik, Vol. J,, pp. 344-384, and Baedeker's Elektrische 
Efscheln^ngen in Metalllschen Leitern, Vieweg, Braunsc|w|.g <19n). 

» Lewis, Adams and Lanman, /. Am. Chem. Soc. 37, ^bob (.laJ-o;. 



386 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

conclusions as to the part which the positive constituent plays in metallic 
conduction. It appears probable, however, that in suitable metallic 
systems an appreciable transfer of matter accompanies the passage of 
the current. 

The view that the conduction process in metals is an ionic one is the 
only one in agreement with our present notions regarding the constitu- 
tion of matter. The absence of material effects accompanying the trans- 
fer of electricity indicates a common carrier in all metallic substances. 
The fact that no positively charged carrier of sub-atomic dimensions is 
known lends probability to the view that metallic conduction is due to 
the motion of the negative electron, the only known carrier of sub-atomic 
dimensions. 

Direct evidence in support of the electron theory of metallic con- 
duction is very meager. Tolman and Stewart " have studied the current 
flow induced in metallic conductors under acceleration. From their meas- 
urements, they have calculated the ratio of the effective mass of the 
carriers to the quantity of electricity flowing. Their results indicate that 
the current is due to the motion of a negative carrier, the ratio of whose 
mass to the charge corresponds with that of the negative electron. For 
copper, aluminum and silver conductors, Tolman and Stewart found for 
the value of 1/m, assuming = 16, the values 1660, 1590, and 1540 
respectively. These are somewhat lower than corresponds to the mass 
of a slowly-moving negative electron, but the difference lies within the 
limits of experimental error. The results of investigations on the prop- 
erties of solutions of the alkali metals in liquid ammonia, described in 
the preceding chapter, likewise furnish striking evidence in support of 
the electron theory of metallic conduction. Other properties of the 
metals, such as the Hall effect, and particularly the emission of negative 
electrons by metals at higher temperatures, lend support to this theory. 
The precise nature of the conduction process of metals, however, still 
remains very obscure. 

3. The Conductance of Elementary Metallic Substances. The 
order of magnitude of the conductance of metals, in itself, furnishes 
evidence in support of the electron theory of metallic conduction. In 
Table CLIII are given values of the atomic conductance and the spe- 
cific resistance, as well as of the mean temperature coefficient a of the 
resistance of a number of elementary metals. 

'Tolman and Stewart, Phya. Rev. 8. 97 (1916) ; ma., 0. 164 (1917), 



THE PROPERTIES OF METALLIC SUBSTANCES 387 

TABLE CLIII. 

Atomic Conductance, Specific Resistance and Resistance Tempera- 
ture Coefficient of Elementary Metals at 0°. 

Metal Ax 10-0 <SoXW ao-,„„X10' 

Silver 6.999 1.468 4.10 

Potassium 6.503 6.100 5 5 

Sodium 5.288 4.28 5.1 

Rubidium 4.845 11.60 

Copper 4.559 1.561 4.33 

Gold 4.547 2.197 3.98 

Caesium 3.898 18.12 

Aluminium 3.834 2.563 4.26 

Magnesium 3.215 4.355 3.90 

Chromium 2.989 4.40 

Calcium 2.457 10.50 

Indium 1.905 8.370 4.74 

Cadmium 1.875 10.023 4.24 

Rhodium 1.811 4.700 4.43 

Zinc 1.713 5.751 4.17 

Lithium 1.534 8.550 4.57 

Iridium 1.414 8.370 3.71 

Tantalum 1.339 14.60 3.47 

Tin 1.252 13.048 4.47 

Osmium 1.119 9.500 4.2 

Thallium 0.9775 17.633 5.17 

Nickel 0.9613 12.323 4.87 

Lead 0.9222 20.380 4.22 

Palladium 0.9082 10.219 3.77 

Platinum 0.8314 11.193 3.92 

Iron 0.8031 9.065 6.57 

Strontium 0.7194 24.75 

Cobalt 0.7064 9.720 3.66 

Manganese 0.6561 4.400 

Antimony 0.4658 39.00 4.73 

Arsenic 0.3735 35.10 3.89 

Gallium 0.2208 53.40 

Bismuth 0.1972 108.00 4.46 

Mercury 0.1564 95.80 0.88 

As may be seen from the table, the specific resistance of silver is 
1.47 X 10" Compared with this, the specific resistance of fused salts 
is of the order of 1.0 and that of electrolytes, at normal concentration, 10. 
In comparing the conducting power of metals it is more rational to 
employ the atomic, or perhaps even the equivalent, rather than the spe- 
cific conductance, On this basis, metallic conductors exhibit many rela- 



388 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

tionships which otherwise are not apparent.^ The atomic conductance 
of potassium and of silver is of the order of 6 X 10" and that of mercury 
at ordinary temperatures, which is a relatively poor conductor, 1.5 X 10^. 
Compared with these values, the equivalent conductance of fused salts 
is in the neighborhood of 50 and that of electrolytes at low concentra- 
tions 100. In a few instances, the equivalent conductance of electrolytes 
is considerably higher, as, for example, in aqueous solutions at high tem- 
peratures, where it approaches a value of 1000, and in solutions of the 
alkali metals in liquid ammonia at low concentrations. The above values 
relate to the conductance of metals at ordinary temperatures. If a simi- 
lar comparison were made at lower temperatures, the relative conduct- 
ing power of the metals would be found to be enormously greater. The 
conductance of metals at very low temperatures will be discussed in 
the next section. 

The conductance of elementary metals in the liquid state is, in gen- 
eral, lower than in the solid state. The process of fusion is accompanied 
by a discontinuous change in the conductance values. In the following 
table are given the ratios of the specific conductances [x^ /(j.^ of metals 
in the solid and liquid states, together with the ratio of their specific 
volumes Vi/v^. 

TABLE CLIV. 

Change of the Specific Conductance of Elementary Metals 

ON Melting. 

Specific 
Conductance 
Melting at the 

Metal Point Melting Point [i^/n^ vi/v 

Lithium... 177.8° 2.6X10* 2 51 

Sodium 97.6 9.5X10* 1.34 1024 

Potassium 62.5 7.7 X 10* 1.39 1 024 

Caesmm 26.4 2.54X10* 1.65' 1027 

Zmc 419. 2.7X10* 2.0 >1 

Cadmium 321. 2.9 X 10* 1.96 1 047 

^ercury -38.8 1.10X10* 4.1 LOSS 

Thallium 301. 1.35X10* 2 

T™ 232. 2.1X10* 2.2 1.028 

^^t^ 327. 1.06X10* 1.95 1.034 

Antimony 629.5 0.88X10* 70 

Bismuth 269. 0.78 X 10* o!46 0.967 

(1916)^'*^'^' ^*"'""'' •'■ ""'"'''■ ^''*"'- "' ^^'^ <^^°®' ' Benedicks, Jahrb. f. Ra4. IS, 35X 



THE PROPERTIES OF METALLIC SUBSTANCES 389 

As may be seen from the table, expansion of the metal on melting is, in 
general, accompanied by an increase of resistance. The change in the 
specific conductance is particularly marked in the case of mercury. In 
the case of antimony and bismuth, the specific conductance increases on 
fusion. This is particularly marked in the case of bismuth, which 
expands on fusion. 

A change in state of an elementary metal is at times accompanied by 
a discontinuous change in the conductance values and at times only by 
discontinuity in the temperature coefficient. The transition from gray 
tin to ordinary tin is doubtless accompanied by a discontinuous change 
in resistance, although the specific conductance of gray tin appears not 
to have been determined. In the case of elementary metals of very low 
conducting power, such as metallic silicon, discontinuous changes in the 
conductance curve have been observed. In other cases, as, for example, 
the transition of the magnetic metals at the recalescence point, the resist- 
ance curve itself is continuous, but the temperature coefficient under- 
goes a discontinuous change, as we shall see below. 

4. The Conductance of Elementary Metals as a Function of Tem- 
perature. The electrical properties of different solid elementary metals 
are strikingly similar. With increasing temperature, the resistance of 
elementary metals increases, the mean coefficient having a value in the 
neighborhood of 0.004, which does not differ greatly from the coefficient 
of expansion of gases at low pressures. Certain metals, as, for example, 
the magnetic metals iron and nickel, have coefficients much higher than 
this value, particularly at higher temperatures. The resistance of most 
metals increases approximately as a linear function of the temperature, 
and over larger temperature ranges the resistance may be expressed very 
nearly as a function of the temperature by means of a quadratic 
equation. 

With decreasing temperature, the resistance of pure metals decreases 
and, down to liquid air temperatures, it would appear that a value of 
zero is being approached as a limit at the absolute zero. The experi- 
ments of Kammerlingh Onnes at liquid helium temperatures, however, 
have brought to light the remarkable fact that at very low temperatures 
the resistance of pure metals undergoes a discontinuous change. When 
a certain temperature is reached, the resistance falls off abruptly to 
values which are almost negligible, if not actually zero.^ For example, 
at 4.24° K. the resistance of mercury in terms of its value at 0° (extrapo- 

» Kammerlingh Onnes, numerous papers in the Proceedings of the Koninklijlte Aljad- 
emie van Wetenschaften te Amsterdam. A summary of the work relating to the properties 
of metals at low temperatures will be found in articles by J. Clay, Jahrbuch der Radio- 
aktivitat und Elektronik n, 259 (1915) ; iUd., 8, 383 (1911) ; see also, Crommelin, Phya. 
Ztachr. 21, 274, 300 and 331 (1920). 



390 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

lated) is 0.163, while at 4.185° the resistance is less than 10-^ and at 
2.45° less than 2 X 10"". Similarly, the resistance of tin vanishes at a 
temperature of 3.78° K. and that of thallium at 2.3° K. The resistance of 
lead vanishes at a temperature between 4.3° and 20°, probably in the 
neighborhood of 6° K. Metals in a condition in which their resistance 
vanishes are said to be in a supraconducting state. Certain metals, such 
as platimmi and copper, do not exhibit supraconductance. In such 
metals the conductance falls to a low limiting value, after which it 
remains independent of temperature. In the following table are given 
values for the resistance of platinum in arbitrary units, at a series of 
temperatures. 

TABLE CLV. 

Resistance of Platinum at Low Temperatures. 

T abs. Resistance 



273.1 


1.0 


20.1 


0.0170 


14.3 


0.0136 


4.3 


0.0119 


2.3 


0.0119 


1.5 


0.0119 



It is apparent from this table that at a temperature in the neighborhood 
of 4.3° absolute the resistance of platinum falls to a value a little greater 
than 0.01 of its value at 0°. Below this temperature, the resistance 
remains constant. Similar results have been obtained for other metals 
such as copper and iron. Apparently, those metals, which exhibit a 
marked tendency to form solid solutions with other metals, do not 
exhibit the phenomenon of supraconductance. It has been suggested 
that the absence of this phenomenon in these metals is due to the influ- 
ence of minute traces of impurities. 

The significance of the phenomenon of supraconductance is not fully 
understood as yet. Various theories have been proposed in explanation 
of this phenomenon, as, for example, that of J. J. Thomson.^ Bridg- 
man " has recently suggested that a polymorphic change takes place at 
the point where supraconductance intervenes. According to this view, 
the normal state of a substance, or of a crystal, at very low temperatures 
is that of supraconductance. The residual resistance found in the case 
of such metals as platinum is due to non-homogeneity between the sur- 
faces of the individual crystals of which the conductor is composed. At 

•J. J. Thomson, Phil. Mag. 30, 192 (1915) 
" Bridgman, J. Wash. Acad. U, 455. 



THE PROPERTIES OF METALLIC SUBSTANCES 391 

the present time it is not possible to reach any certain conclusion as to 
the nature of these phenomena. 

The mean temperature coefficients a for a number of elementary sub- 
stances are given in Table CLIII above. In the following table are 

1 (IT? 
given values of the temperature coefficient a = — -j-^ for a number of 

Rf at 
metals at different temperatures. 



TABLE CLVI. 

1 dR^ 

Tempekattjee Coefficient — -j— for Metals at Different 

Tem peratures . 
Temperature Ag Fe Ni Al Mg Cu 

25° 0.0030 0.0052 0.0043 0.0034 0.0050 0.0036 

100 0.0036 0.0068 0.0043 0.0040 0.0045 0038 

200 0.0039- 0.0090 0.0070 0.0042 0.0041 0040 

300 0.0040 , 0.0111 0.0080 0.0043 0.0043 0041 

400 0.0042 0.0133 0.0036 0.0046 0.0040 0042 

500 0.0044 0.0147 0.0030 0.0050 0.0036 0.0043 

600 0.0046 0.0170 0.0028 0.0060 0.0100 0044 

700 0.0Q47 0.0224 0.0026 0.0120 0.0250 0047 

800 0.0052 0.0120 0.0025 at 625° at 625° 0.0053 

900 0.0058- 0.0046 0.0028 • • • • 0057 

1000 0.0050 0.0037 .. .. 0062 

1075 .. 0.0062 

It will be observed, from the table, that the temperature coefficient in- 
creases with increasing temperature. The magnitude of the coefficients 
of different metals differs considerably, particularly those of the magnetic 
metals, iron and nickel. It is interesting to note that, as the transition 
point of these metals is approached, the temperature coefficient increases 
very largely. The temperatures at which the transition points are 
reached are indicated in the table by heavy type. Beyond the transition 
points, the temperature coefficients fall back to normal values, in the 
case of both iron and nickel. A somewhat similar phenomenon is ob- 
served in the neighborhood of the melting point, which is illustrated in 
the case of aluminium and magnesium, particularly in the case of the 
latter element. The temperature coefficient increases considerably as the 
melting point is approached. Beyond the melting point, the coefficients 
are, in general, smaller than below this temperature. 

The temperature coefficients of elementary liquid metals vary within 



392 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

wide limits. The coefficients are greatest for the alkali metals, in which 
case they differ very little from those of the solids. In other cases, the 
temperature coefficients reach extremely small values, as, for example, 
in that of zinc. As a rule, the temperature coefficients of liquid metals 
have values in the neighborhood of one fifth that of the solid metals. In 
the following table are given the mean temperature coefficients of a 
number of liquid inetals referred to their resistance at the lowest tem- 
perature given. 

TABLE CLVII. 

Temperature Coefficient of Liquid Metals. 

Temperature 
Metal a Interval 

Sodium 38.5 X 10"* M.P. 

Potassium 41.8 X 10"* " 

Lithium 27.3 X 10"* 178-230 

Tin 5.9 X 10-* M.P.-350 

Bismuth 4.1 X 10"* " 

Thallium 3.5 X 10"' " 

Cadmium 1.3 X 10-* " 

Lead 5.2 X 10"* " 

Copper 4.12 X 10'* 1084r-1500 

Aluminium 5.42 X 10"* 653-1250 

Iron 3.66 X 10-* 1055-1650 

Nickel 1.67 X 10-* 1451-1650 

Zinc 0.3 X 10-* 41^-500 

Tin 4.68 X 10"* 232-1600 

Cadmmm 2.26 X 10"* 500-650 

Antimony 1.37 X 10* 631-800 

The temperature coefficients here given cannot be directly compared 
with those of the solid metals at ordinary temperatures, since the coeffi- 
cients are referred to the resistance of these metals at higher tempera- 
tures. In a number of instances values have been extrapolated to ordi- 
nary temperatures, in which case the coefficients are invariably smaller 
than those of solid metals. For example, the values for copper 
aluminium and iron are 7.45 X 10"*, 8.40 X 10-* and 8.15 X 10"*, re- 
spectively. 

The temperature coefficient as commonly measured is the resultant 
effect of temperature change and volume change. The temperature coef- 
ficient at constant volume differs materially from that at constant pres- 
sure, depending upon the influence of pressure upon the resistance of the 
conductor in question. In solid metals, the pressure effect is relatively 



THE PROPERTIES OF METALLIC SUBSTANCES 393 

small, while the resistance-temperature coefficient is large; consequently, 
the temperature coefiScient is not greatly affected by the volume change. 
In liquid metals, however, where the temperature coefficient is small and 
the resistance pressure coefi&cient relatively large, the volume change has 
a material influence on the observed temperature coefficient. In the case of 

mercury ,^^ the resistance temperature coefficient! „ )( ^- 1 = — 6.9X 10* 



as against the value of + 8.9 X 10"* for the resistance-temperature coeffi- 
cient at constant pressure. It is a significant fact that the resistance of 
a liquid metal at constant volume should decrease with increasing tem- 
perature. In this connection it may be noted that Somerville ^^ found 
that zinc wire, wrapped in the form of a spiral around a silica tube, 
exhibited a marked negative temperature coefficient above the melting 
point, the resistance varying very nearly as a linear function of the tem- 
perature. In this case the metal in the fluid state was held together by 
surface forces. The temperature coefficient of molten zinc in a quartz 
tube was found to be positive but of a very low value. 

5. The Conductance of Metallic Alloys. Metallic alloys may be 
divided into four classes which exhibit distinct properties.^^ These are: 
First, solid alloys in which pure crystals of the constituent elements are 
present in intimate contact; second, solid alloys in which mixed crystals 
of the constituent elements are present; third, solid alloys in which com- 
pounds of the constituent elements are present; and fourth, liquid alloys. 
Among the solid alloys, several of these types often appear in a single 
alloy. This is the case, for example, when mixed crystals are formed 
over limited concentration intervals. 

a. Heterogeneous Alloys. Except in so far as the resistance of alloys 
is influenced by the distribution of the crystals and the presence of resist- 
ance at the interface between crystal elements, solid alloys of the first 
class do not differ in their properties from pure metals. The specific 
resistance of such alloys is a linear function of the composition and with 
change of temperature the properties vary as a linear function of the 
composition. 

b. Homogeneous Alloys. Homogeneous mixed crystals of pure 
metallic elements, or of compounds, form an important class of substances 
which are remarkable for the uniformity of their behavior among them- 
selves and the divergence of their behavior from that of their constituent 
elements. The addition of a second metallic component to another metal, 

"Kraus, Physical Review \, 159 (1914). 

" Somerville, Physical Review 33, 77 (1911). , t i t. , n ^ ^ 

" A summary of the properties of metallic alloys is given by Guertler, Jahri. f. Pad. S, 

17 (1908). 



394 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

whether elementary or compound, causes a marked decrease in the con- 
ductance of the resulting homogeneous alloy. The decrease due to the 
addition of a given amount of the second constituent is the greater the 
lower its concentration. If the conductance is represented graphically 
as a function of the composition of the system, the resulting curve is 
throughout convex toward the axis of concentration. The minimum 
point in all cases lies in the neighborhood of a composition of 50-50. In 




O 

Au 



20 UO 60 80 

Composition, volume per cent. 



100 

Ag 



Fig. 68. Representing the Conductance of Homogeneous Alloys of Ag and Au as a 

Function of Composition. 



Figure 68 is shown the conductance curve at ordinary temperatures for 
homogeneous mixtures of silver and gold. As may be seen, the conduct- 
ance of either component is greatly reduced on the addition of the second 
constituent. The decrease in the conductance due to the addition of a 
second component depends upon the nature of the substance added and is, 
in general, the greater the less electropositive the added constituent. 
Thus, the decrease in the conductance of iron due to the addition of 
carbon or silicon is much greater than that due to the introduction of 



THE PROPERTIES OF METALLIC SUBSTANCES 



395 



tungsten or nickel. On the other hand, certain variations occur in the 
order of the effects. Thus, due to the addition of aluminium, the con- 
ductance of iron is lowered very nearly as much as due to that of silicon. 
The resistance-temperature coefficient of solid alloys of the second 
class likewise varies continuously as a function of composition. The 
curve of temperature coefficients is similar to the conductance curve, being 
convex toward the axis of concentration and having a minimum point in 
the neighborhood of a composition of 50-50. In Figure 69 is shown the 
curve of temperature coefficients for alloys of silver and gold. It will 



o 

o 



0.OC4 






















1 


















, 


0003 


^ 


















-j 


O.OOZ 
0.00J 


\ 


\! 
















J- 



































^ O 10 t» so ICO 

Hg *" 

Composition, volume per cent. 

Fig. 69. Temperature Coefficient of Silver-Gold Alloys as a Function of Composition. 

be observed that the temperature coefficient falls from a value of approxi- 
mately 4 X 10"^ for the pure elements to 7.5 X 10"* for an alloy contain- 
ing 50 volume per cent, each, of the constituents. This behavior of homo- 
geneous metallic alloys is general. In many cases, the effect is very 
pronounced and the temperature coefficient falls to very low values. 

With decreasing temperature, particularly at low temperatures, the 
resistance of homogeneous metallic alloys decreases nearly as a linear 
function of the temperature. This form of the curve persists even to the 
lowest temperatures attainable. Apparently, then, the resistance of 
alloys of this type approaches a finite limiting value at the absolute zero. 
In the following table are given values of the resistance of manganin wire 
(84 Cu, 12 Mn, 4 Ni) down to liquid helium temperatures. 

TABLE CLVIII. 
Resistance of Manganin Wire at Low Tempeeatuees. 



Temp. 
Resist. 



16 5 —193.1 —201.7 —253.3 —258.0 —269.0 —271.5 
124.20 119.35 117.90 113.42 112.91 111.92 111.71 



396 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

Other alloys of this type exhibit a similar behavior at low temperatures. 

At high temperatures, the resistance curves of many of the alloys of 
this type are very complex, often exhibiting both maxima and minima 
and the temperature coefficient at times becoming negative.^'* The curve 
for manganin wire, for example, exhibits two maxima at approximately 
25° and 475° C. and two minima at 360° and 525° C. respectively. In a 
few instances, the temperature coefficient is very nearly zero over a large 
range of temperature, as, for example, in the case of advance wire, for 
which the temperature coefficient varies very little up to a temperature of 
250° C. Taken all together, the resistance curves of solid solutions of 
metals are very complex at higher temperatures. 

c. Solid Metallic Compounds. The conductance of a solid compound 
of two elements is always lower than that of one of the constituents and 
is often lower than that of both. The specific resistance of a compound 
relative to that of the constituent elements depends upon the nature of 
the elements and upon tne nature of the compound formed. In general, 
the more stable the compound, the higher is its resistance relative to 
that of the constituent elements. Compounds between strongly electro- 
positive and strongly electronegative metallic elements, as a rule, exhibit 
a very high specific resistance. In the following table are given values 
of the specific conductance of a number of compounds at room tem- 
peratures. 

TABLE CLIX. 

Specific Conductance of a Number of Metallic Compounds. 

Metal Mg^Sn Cu.Mg CuMg, MgZn, Mg3Bi3 ALMn ALFe 

[iXlO-* .. 0.0912 19.4 8.38 6.3 0.76 0.20 0.71 

Metal Al3Ni AlMg Al,Mg3 Al,Ag3 AlAgj Sb.Te, TeSn 

\x X 10-* . . 3.47 2.63 4.53 3.85 2.75 0.48 0.97 

Metal Bi^Tcg SbAg3 Cu^As MgAg Mg,Ag 

fiXlO-* .. 0.045 0.93 1.70 20.52 6.16 

It will be observed, from the table, that the compound between mag- 
nesium and tin has a very low specific conductance. Where two ele- 
ments form a number of different compounds, that compound, in gen- 
eral, has the lowest specific conductance which corresponds to the normal 
electronegative valence of the less metallic element. Thus, the specific 
conductance of Cu.Sn is much lower than that of CUjSn or of CuSn 
The low value of the specific conductance is well shown in the case of the 
alloys of magnesium and tin which form the compound, Mg^Sn. The 

"" Somerville, Phya. Rev. 31, 261 (1910). 



THE PROPERTIES OF METALLIC SUBSTANCES 397 

specific conductance of this compound at 25° is 0.0912, as compared with 
8.65 for tin and 22.73 for magnesium. 

While the conductance of inter-metallic compounds is thus, in gen- 
eral, very low, the temperature coefficient of these compounds is of the 
same order of magnitude as that of pure metals. While, therefore, the 
addition of a second metallic component increases the resistance of the 
metallic alloy, whether a compound or a solid solution is formed, so that 
it is at times difficult to distinguish between these two cases by this 
means, the temperature coefficient of the resulting alloy will, in general, 
differ widely in the two cases. The high value of the temperature coeffi- 
cient of metallic compounds and the low value of this coefficient for 
homogeneous alloys afford a delicate method of detecting the presence 
of solid solutions in metallic alloys. 

d. Liquid Alloys. The properties of liquid alloys differ greatly from 
those of homogeneous solid alloys. On the addition of a second com- 
ponent, the conductance of a liquid metal may either increase or de- 
crease. The relative conductance of the two substances does not deter- 
mine the magnitude and sign of the initial conductance change. If the 
specific conductance of two metals is nearly the same, the conductance 
curves often exhibit maxima or minima and sometimes both maxima and 
minima. In Figure 70 are shown the conductance curves for mixtures 
of mercury with bismuth, lead, tin and cadmium. Small additions of 
these elements to mercury cause a relatively large initial rise of the 
conductance curve. This rise is particularly noteworthy in the case of 
bismuth, which itself is a relatively poor conductor. The four curves are 
evidently similar. With bismuth and lead, whose specific conductances 
are relatively low, both a maximum and a minimum occur in the con- 
ductance curve. With tin the maximum and minimum have disappeared, 
but an inflection point is present in the conductance curve. The curve 
for alloys of cadmium and mercury exhibits a constant curvature. The 
four elements, the conductance of whose amalgams are shown in the 
figure, do not form compounds with mercury according to their melting 
point diagrams. 

The behavior of amalgams, in which compounds are formed, differs 
markedly from that of amalgams in which compounds are absent. The 
addition of small amounts of lithium, calcium and strontium increases 
the conductance of mercury, while that of potassium, sodium, caesium 
and barium reduces its conductance." With increasing temperature, the 
relative effect of such addition is increased. According to Hine," the 

" TT Fennineer, Dissertation, Freiberg, 1914 ; J. Koenigsberger, loc. cit., p. 654. 
«Hine, J. Am. Chem. Soc. S9, 890 (1917). 



398 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

specific conductance of sodium amalgams passes through a minimum at 
about 2.5 atom per cent of sodium. McCoy and West "- have determined 
the conductance of amalgams of substituted ammonmm bases. The 
conductance of these amalgams decreases with increasing concentration, 
passing through a minimum. In general, liquid alloys whose components 
do not form compounds exhibit conductance curves without pronounced 
minima. On the other hand, alloys which form compounds often exhibit 
pronounced minima. This is, for example, the case with alloys of sodium 
and potassium. In the following table are given conductance values of 
mixtures of sodium and potassium, together with their temperature coeffi- 
cients.^^ 

TABLE CLX. 

Conductance of Liquid Sodium-Potassium Alloys at 200°. 

Specific 

Atom Per Cent Conductance 

Potassium ^ X 10* a X 10' 

7.37 4-3.85 

4 2 5.55 3.222 

8.0 4.42 2.43 

26.5 2.690 1.725 

44.5 2.150 1.555 

63.0 2.095 1.585 

82.0 2.250 1.860 

93.0 3.230 2.91 

100.0 4.59 4.98 

It will be observed that the conductance curve exhibits a minimum in 
the neighborhood of 50 atomic per cent of sodium and potassium, which 
corresponds with the composition of the compound NaK. The existence 
of this compound has been estabhshed by means of the melting point 
diagram. It will be observed, also, that the temperature coefficient of the 
sodium-potassium alloys exhibits a minimum value at a composition cor- 
responding with that of the compound. The conductance of alloys of 
copper and lead exhibits neither a maximum nor a minimum, but the tem- 
perature coefficient exhibits a minimum at a composition in the neighbor- 
hood of 40 per cent of lead. The conductance curves of liquid alloys of 
copper and antimony exhibit singularities corresponding with the com- 
position of the compounds Cu^Sb and CugSb. The temperature coeffi- 
cients of both these compounds are negative, while those of the pure 
metals are positive. The conductance curve for liquid mixtures of copper 

""McCoy and West, J. Phys. Chem. 16, 861 (1912), 
" Koenigsbei'ger, foe. qU, 



THE PROPERTIES OF METALLIC SUBSTANCES 399 

and tin likewise exhibits singularities, which indicate the formation of 
compounds. The temperature coefficients of these compounds are 
negative. 

It may be concluded that liquid alloys, in which compounds are 
formed, exhibit properties which differ markedly from those of alloys in 
which compounds are not formed. When the compounds formed are 
very stable, the conductance of the resulting alloy is usually less than 
that of the pure components. The temperature coefficient of fused metal- 
he compounds is, as a rule, either very small or negative. 




C fO 20 JO W SO 60 70 80 90 700 

Hg B 

Weight Per Cent B 

Fig. 70. Conductance of Liquid Amalgams as a Function of Composition. 



6. Variable Conductors. Within this class are included those ele- 
mentary substances which lie upon the border line between metallic and 
nonmetallic elements. There are also included a considerable number 
of metallic compounds in which one of the constituents is strongly electro- 
negative. The elementary substances comprised within this class often 
appear both in a metallic and in a nonmetallic state. Carbon is a typi- 
cal example of this type which, in the form of diamond, is a noncon- 
ductor, and, in the form of graphite, a relatively good conductor. Many 
of the metallic compounds, also, may appear both in a conducting and in 
a nonconducting state, as, for ejcample, various sulphides and oxides 



400 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

which are metallic in a crystalline state and which are nonmetallic 
when precipitated from solution. 

The specific conductance of the metals of this class is often relatively 
low. In the following table are given values of the specific conductance 
of a few of these metals. 

TABLE CLXI. 

Specific Conductance of Various Substances at 0°. 

Conductor Specific Conductance 

Graphite (Siberia) 8.71 X 10' 

Silicon (+ 3.3% impur.) 10.0 

Titanium 2.8 X 10' 

Zirconium 5 X lO' 

CuS 8.5 X 10' 

PbO^ 4.3 X 10' 

CdO 8.3 X 10' 

PbS 4.2 X 10' 

Fe^O, 1.16X10' 

FeS^ (Pyrite) 0.42X10' 

FeS^ (Marcasite) 0.06 

The resistance of metals of this class at lower temperatures decreases 
greatly with increasing temperature, approximately as an exponential 
function. At higher temperatures, the conductance reaches a minimum 
value, after which it increases approximately as a linear function of the 
temperature. A familiar example of this type of substance is carbon. 
It is uncertain, however, that the observed conductance curves of this 
type actually relate to pure substances. Kammerlingh Onnes and Hof " 
have shown, for example, that graphite may be purified to a point where 
its resistance decreases with temperature down to approximately — 173° 
with a coefl[icient of 0.0029. At lower temperatures the resistance de- 
creases somewhat more rapidly. Similar results have been obtained in 
the case of bismuth. In the earlier experiments of Dewar and Fleming,^* 
bismuth was found to exhibit a minimum resistance at temperatures 
varying from room temperatures to — 80° C, depending upon the purity 
of the sample. Later, however, this element was purified to a point where 
its resistance decreased throughout with decreasing temperature down to 
liquid hydrogen temperatures." Since many of the substances of this 
class cannot be prepared readily in a pure state, it follows that the pecu- 

" K, Onnes and Hof, Konmklljke Akad, van Wctensch. Amsterdam n. 520 (1914) 

"Dewar and Fleming, Phil. Mag. J,0, 303 (1895). 

"J. Clay, Dissertation, Leiden (1908) ; JahrTy. ]. Bad. 8, 391 (1911). 



THE PROPERTIES OF METALLIC SUBSTANCES 401 

liar form of the conductance curve may be due primarily to the presence 
of impurities. 

Many of these substances exhibit transition points at which the resist- 
ance changes discontinuously. In some instances these processes are 
reversible and in others irreversible. Silicon exhibits transition points 
at approximately 220° and 440°. Titanium exhibits discontinuities in 
the neighborhood of 300° and 600°, the first of which is slowly reversible 
and the second irreversible. 

Among variable conductors are included many compounds on the 
borderline between metallic and nonmetallic substances. These com- 
pounds often appear in several modifications whose properties may differ 
greatly. For example, silver sulphide, which has already been mentioned 
in a preceding chapter, conducts electrolytically in one form, while in 
another form it exhibits mixed electrolytic and metallic conduction. 
Many solid oxides and mixtures of oxides, which at ordinary temper- 
atures are nonmetallic, appear to conduct the current metallically at 
high temperatures. The Nernst filament is a familiar example of this 
type of conductor. While it is possible that a portion of the current in 
some of these substances is carried electrolytically, the greater portion 
appears to be carried metallically. 

As the compounds become more distinctively metallic, which is as a 
rule the case as the more electronegative element becomes more metallic 
and the more electropositive element becomes less metallic, the conduct- 
ance approaches that of typical metallic compounds. In such cases, the 
temperature coefiicient becomes less negative or even positive. In gen- 
eral, the higher the conductance of a compound, the greater is the value 
of its positive temperature coefiicient. 

Many of the conductors belonging to this class exhibit singular prop- 
erties. In many cases, also, systems, which might not be expected to 
exhibit metallic properties, nevertheless belong to this class of conductors. 
Such is, for example, the case with cuprous iodide, Cul, which absorbs 
iodine reversibly. The resulting product conducts the current metal- 
lically and its conductance is the greater the greater the amount of iodine 
absorbed. The smaller the resistance of the iodide, the greater is the 
value of the positive temperature coefficient. As the specific resistance 
increases, the temperature coefficient becomes negative. 

The examples of this class of substance are extremely numerous and 
a great deal of experimental material is available. It is not to be doubted 
that a study of such systems will throw a great deal of light on the nature 
of the conduction process and conceivably on the constitution of metallic 



402 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

compounds. A more detailed discussion, however, is not possible in this 
monograph.^" 

7. The Conductance of Metals as Affected by Other Factors. 
a. Anisotropic Metallic Conductors. As might be expected, the con- 
ductance of many crystalline substances depends upon the orientation of 
the crystal. Thus, the conductance of a crystal of bismuth at right 
angles to its base at 15° is 1.78 times that parallel to its base.^^ It has 
been shown that the conductance of a bismuth crystal may be represented 
by means of an ellipsoid of rotation.^^ 

b. Influence of Mechanical and Thermal Treatment. The conduct- 
ance of metals is dependent upon their previous mechanical and thermal 
treatment. Wires which are hard drawn in general exhibit a lower con- 
ductance than do annealed wires. The thermal treatment of metals has 
an influence on their conductance, not only in that it tends to relieve 
mechanical stresses resulting from previous mechanical treatment, but 
also in that it tends to induce various transformations in the body of the 
metal, some of which are reversible and others of which are irreversible. 

c. The Influence of Pressure on Conductance. The resistance of 

most metallic elements is decreased under the action of uniform pressure. 

1 d7? 
The coeflBcient ^ -i- for solid metallic elements varies between— 15.1X10'^ 
it dp 

for nickel and — 152 X lO"' for lead. For bismuth the value of the 
coefficient is positive and equal to + 196 X 10'''. The resistance does 
not vary as a linear function of the pressure, the pressure coefficient de- 
creasing with increasing pressure. The resistance of manganin wire 
varies very nearly as a linear function of the pressure. The only pure 
liquid metal for which data are available is mercury. At 25°, the value 
of its resistance-pressure coefficient is — 334 X lO"''. It would be inter- 
esting to know whether other liquid metals exhibit a similarly high value 
of this coefficient. 

The influence of pressure on the resistance of variable conductors is 
often extremely marked.^^ 

d. Photo-electric Properties. A few substances are sensitive to the 
action of light. Selenium is the most remarkable example of this type 
of substances. The influence of light and various other factors on the 
conductance of selenium has occupied the attention of a great many inves- 
tigators. A detailed discussion cannot be given here.^* 

8. Relation between Thermal and Electrical Conductance in Metals. 

a»A very complete summary is given by Koenigsberger, loo. cit.. pp. 661-680 
"i'Lownds, Ann. d. Fhye. 9, 681 (1902). f . ^- <-■■•■•. vv- odj. oou. 

22 van Everdingen, Versl. Aka4. van Wetensch. Amsterdam s, 316 and 407 (1900) 
='For references, see Koenigsberger, loc. cit., pp. 694-7 k'^o'J'ji, 

" For references, see Koenigsberger, Joe. cit., pp. 681-694, 



THE PROPERTIES OF METALLIC SUBSTANCES 403 

As was first pointed out by Wiedemann and Franz," the thermal con- 
ductance of metals at ordinary temperatures is very nearly proportional 
to their electrical conductance. Subsequent investigations ^^ have shown 
that the ratio of thermal to electrical conductance is not a constant, but 
increases with increasing temperature. Lorenz " showed that the ratio 

3l 
of thermal to electrical conductance - for pure metallic substances and 

some alloys increases approximately as a linear function of the absolute 
temperature, the coefficient being very nearly equal to the coefficient of 
expansion of gases. Since the resistance varies approximately as a linear 
function of the absolute temperature, it follows that the thermal con- 
ductance of metals is relatively independent of temperature. At very low 
temperatures, however, the thermal conductance of metals increases 
markedly. Nevertheless, as K. Onnes and Hoist ^^ have shown, the 
thermal resistance of metals does not approach a value of zero in 
regions where metals are in the supraconducting state. For example, at 
its melting point, the thermal conductance of mercury is 0.075; between 
4.5° K and 5.1° K it is 0.27; and between 3.7° K and 3.9° K it is 0.40. 
At very low temperatures, therefore, the thermal and electrical conduct- 
ance do not follow a parallel course. 

The thermal conductance of alloys varies with composition in a man- 
ner somewhat similar to that of the electrical conductance. The change 
in thermal conductance, due to a given change in composition, is consid- 
erably smaller than is the corresponding change in electrical conduct- 
ance. The thermal conductance curves of alloys which form a complete 
series of mixed crystals exhibit a minimum similar to that of the elec- 
trical conductance curves. The relative decrease of the thermal con- 
ductance, however, is much smaller than that of the electrical conduct- 
ance. Accordingly, the ratio of the thermal to the electrical conductance 
for homogeneous alloys is considerably greater than it is for pure metals. 
Somewhat similar relations are found in the case of metallic compounds. 
While compounds in general exhibit a lower thermal conductance than 
do the pure components, the ratio of thermal to electrical conductance is 
larger for the compounds than it is for pure metals. 

The thermal conductance of variable conductors is often as great as 
that of typical metallic elements. Since the electrical conductance of 

these substances is relatively low, the ratio- for these substances is often 



404 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

very great. Thus the value of - for graphite, silicon and hematite 

(Fe^Oj) is 2.5 X 10^^ 6.8 X 10^* and 7.3 X 10^* respectively. For ordi- 
nary metals the value is in the neighborhood of 6.7 X 10^° at room tem- 
peratures.^* In this connection it is interesting to note that the thermal 
conductance of some nonmetallic crystals is greater than that of many 
metallic substances. Thus, the thermal conductance of rock salt is 
0.0137 and that of quartz -l to its axis is 0.0263, while that of bismuth is 
0.0194. While thermal and electrical conductance are intimately related, 
the fact that some nonmetals are likewise excellent thermal conductors 
should not be lost sight of. 

9. Thermoelectric Phenomena in Metals. We have to consider three 
related thermoelectric phenomena, namely: 1, the electromotive force 
arising in a metallic system as a result of a temperature difference be- 
tween the junctions of two metals; 2, the Peltier effect which is a heat 
transfer taking place when a current passes through a junction between 
two different metallic conductors; and, 3, the Thomson effect which is a 
heat transfer accompanying the passage of the current through a con- 
ductor in which a temperature gradient exists. From a practical point 
of view, the first of these effects is the most important and has been 
investigated most extensively. 

The thermoelectric force of a thermocouple may be expressed very 
nearly as a function of the temperature by means of an equation of the 
form: 

e^B =at-\-i^t' + --- 

Usually a quadratic equation sufiBices. For smaller temperature differ- 
ences, the sign of the constant a corresponds with the direction of the 
thermoelectric force. The sign of this electromotive force depends upon 
the nature of the metals. Let us call the effect positive for the two metals 
AB, when the current flows from A to B at the cold junction. The metal 
A will then be said to be positive with respect to B. The values of the 
coefficients a and p for different metals with respect to lead, the cold 
junction being kept at a temperature of 0° C, are given in Table CLXII. 
As may be seen from the table, metals which are closely related often 
have thermoelectric constants which are opposite in sign; thus, lithium 
and potassium stand in reverse order to lead, which, in the table, is taken 
as a standard. So, also, the closely related elements, antimony and 
bismuth, which exhibit a relatively high thermoelectric power, lie near 

" See EoenlgBberger, loc, <Ht., p. 720. 



THE PROPERTIES OF METALLIC SUBSTANCES 405 

TABLE CLXII. 

Values op the Thermoelectric Coefficients a and p with Respect 
TO Lead in Microvolts per Degree. 

Metal Si Te^^^ Sb|| Fe Li Ag Pb 

a +443 + 163 + 22.6 + 13.4 + 11.6 + 2.3 

PXIO^ —3.0 +3.9 +0.76 

Metal Mg Sn Na K Co Ni Bi|| 

a —0.12 —0.17 —4.4 —11.6 —20.4 —23.3 —127.4 

pXlO^ •• +0.20 +0.20 —2.1 —2.5 —7.5 —0.8 —70. 

the opposite ends of the table. Similar inversions are found in the case 
of other closely related elements, such as iron, cobalt and nickel. 

In alloys, the thermoelectric force is, in general, a function of the 
composition. The thermoelectric force of heterogeneous alloys varies 
approximately as a linear function of the composition, while that of 
homogeneous alloys, in general, exhibits a marked minimum somewhat 
similar to that of the conductance curve. The thermoelectric power of a 
compound, in general, differs from that of its component elements. The 
formation of compounds by a given pair of elements is indicated by dis- 
continuities in the curves connecting the thermoelectric force with the 
mean composition of the alloy. As a rule, the thermoelectric force is 
high for compounds which are relatively poor conductors. For a more 
detailed discussion of the thermoelectric properties of metals the reader 
is referred to the various handbooks in which these data have been 
collected. 

10. Galvanomagnetic and Thermomagnetic Properties. When a cur- 
rent of electricity flows through a conductor, , the distribution of the 
current in the conductor is altered under the action of an external mag- 
netic field. The effects observed depend upon the relative direction of 
the current and of the field. The application of the magnetic field, there- 
fore, gives rise to potential differences between points in the conductor 
which normally are at the same potential. With a field acting at right 
angles to the direction of the current flow, potential differences arise in 
the conductor transverse to the magnetic field, one at right angles to the 
direction of the current flow and the other parallel to this direction. 
With a longitudinal field, that is, a field acting parallel to the direction 
of the current flow, only a single effect is observable; namely, an electro- 
motive force parallel to the direction of current flow. Similar effects 
are observed when a current of heat flows through a conductor in a mag- 



406 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

netic field. Conversely, when a current flows through a conductor in a 
magnetic field, temperature differences, as well as potential differences, 
arise in the conductor. Altogether, there are twelve effects of this type: 
four thermomagnetic effects in transverse fields, two thermomagnetic 
effects in longitudinal fields, four galvanomagnetic effects in transverse 
fields, and two galvanomagnetic effects in longitudinal fields. 

Of these various effects, the transverse galvanomagnetic effect in a 
transverse field has been studied most extensively. This is commonly 
known as the Hall effect. The relation between the electromotive force 
and the variables of the system are given by the equation: 

RHi 



e = 



D 



where H is the field intensity, i is the total current flowing, and D is the 
thickness of the conducting sheet carrying the total current i. R, which 
is the constant of the Hall effect, is a property of the conductor in ques- 
tion. This constant varies greatly for different metals and may have 
either positive or negative values. As a rule, the effect is greatest in 
substances of relatively low conducting power. It is particularly marked 
in bismuth. Here, however, as might be expected, the value of the coeffi- 
cient depends upon the orientation of the crystal. Since the flow of 
current in a conductor is influenced by an external magnetic field, it fol- 
lows that the resistance of a conductor will be influenced by an external 
field. 

At low temperatures, the influence of a magnetic field on the resist- 
ance becomes marked, particularly for bismuth. K. Onnes ^° has shown 
that at very low temperatures, where metals are normally in the supra- 
conducting state, the curves connecting resistance and field strength are 
similar to those connecting resistance and temperature. The action of 
transverse and longitudinal fields differs little. For lead and tin the 
critical value of the field strength at which the resistance rises abruptly 
to measurable values lies between 500 and 700 G. It varies slightly with 
temperature. 

The various galvanomagnetic and thermomagnetic effects would ap- 
pear to be of great importance from a theoretical standpoint; for, if a 
current is carried by charged particles, the observed effects must be due 
to the reaction of the field on these particles. It might be expected that 
the reaction of the field on the moving particles in a metallic conductor 
would be similar to that observed in the case of the cathode rays. Actu- 
ally, however, the observed effect in the case of most metallic conductors 

'"Yeral. Akad, van Wetensch. Amsterdam 23, 493 (1914). See also J. Clay, loc. cit. 



THE PROPERTIES OF METALLIC SUBSTANCES 407 

is in a direction opposite to that observed in the case of p particles, assum- 
ing that the conducting particles in metals are negatively charged. Since 
a great many facts indicate that the current in metallic conductors is not 
carried by positive particles, it appears that the various galvanomagnetic 
effects cannot be accounted for by a simple theory of this type. A num- 
ber of theories, that of J. J. Thomson for example, have been suggested 
to account for the Hall effect and similar phenomena.^^ At the present 
time, however, a satisfactory theory of these effects does not exist. In- 
deed, the same may be said of the theory of the conduction process in 
metals under normal conditions. It may be expected, however, that 
ultimately the thermomagnetic and galvanomagnetic effects will play an 
important role in the development of the theory of metallic conduction. 

A detailed study of the properties of conductors in a magnetic field 
would lead far beyond the scope of the present monograph. The ob- 
served facts will be found summarized in the references already given. 

11. Optical Properties of Metals. According to the electromagnetic 
theory, the electrical and optical properties of metallic substances are 
intimately related. The reflecting power and absorbing power of metals, 
according to this theory, should be very great. From the known values 
of the conductance of metallic substances, the optical constants of these 
substances may be derived for long wave lengths when selective action 
does not occur. 

The theory of the optical effects in metals, together with the most 
important facts, will be found summarized in treatises on electricity and 
magnetism and on physical optics."^ 

12. Theories Relating to Metallic Conduction. The theory of metal- 
lic conduction, like the theory of electrolytic conduction, is still in a very 
unsatisfactory state. Qualitatively, the theory that the current is carried 
by negative electrons is in good agreement with the facts, but a satisfac- 
tory quantitative theory has not, as yet, been established. The difficulties 
confronting a comprehensive theory of metallic conduction are, indeed, 
very great, as is apparent when it is considered how many detailed facts 
must be accounted for. A number of theories which have been proposed 
are able to account for a limited number of the properties of metals in a 
fairly satisfactory manner. So, for example, the theories of Drude and 
of Thomson render an account of the relation between the thermal and 
the electrical conductance of metals and, to some extent, also, of the 
thermo- and galvanomagnetic effects and thermoelectric effects in metals. 
On the whole, however, these theories are far from satisfactory. They 

Bi T T Thomson Bavt). Conur. Phys. 3, 143, Paris (1900). 

•^ See for Txample? Winkeiioann, Handbucb d. Physik ; Graetz, Handbuch d. Elek- 
trizitat u.' d. Magnetlsmus, etc. 



408 PROPERTIES OF ELECTRICALLY CONDUCTING SYSTEMS 

are not able to account for the properties of metallic substances at very- 
low temperatures. Neither are they able to account successfully for 
the properties of alloys and of liquid metals.'^ 

It is obvious that the electrical properties of metallic substances are 
extremely sensitive to all agencies. Temperature and density, as well as 
all external forces, have a marked influence upon the electrical properties 
of metals, and particularly on the conductance. So, also, the properties 
of metallic substances are very sensitive to change in the state of the 
system. The formation of compounds, of mixed crystals, or any poly- 
morphic change is invariably accompanied by a great change in electrical 
properties. Ultimately, it would appear that a study of the electrical 
properties of metals, and particularly of metallic compounds, should yield 
some clue as to the constitution of these substances. At the present time, 
however, the constitution of metallic substances, and particularly of 
metallic compounds, remains an unsolved problem. 

" Very complete references to the theories dealing with metallic conduction are given 
by Koenigsberger, loc. cit., p. 385, above. 



SUBJECT INDEX 



Acetone, conductance of C0CI2 in — at dif- 
ferent temperatures, 163 ; — conductance 
of Nal in, 47 ; — values of Ao in, 62 ; — 
values of mass-action constant in, 62 

Acid, acetic, mass-action constant of, 43 ; 

— amides, nature of, 815 ; — formic, hy- 
drolytic equilibria in, 230 ; — formic, 
solution of formates in, 101 ; — sulphuric, 
intermediate ions in aqueous solutions of, 
148 ; — trlchlorobutyrie, mass-action con- 
stant of, 44 

Acids, conductance of — in alcohol-water 
mixtures, 181 

Activity Coefficient of TlCl from solubility 
data, 337 ; — Coefficient, definition of, 
331 ; — Coefficient, numerical values for 
concentrated' solutions, 334 ; — Coeffi- 
cient, numerical values for dilute solu- 
tions, 333 ; — Coefficient, values obtained 
by different methods compared, 334 ; — 
definition of, 331 

Alcohol, ethyl, conductance of Nal In, 47 ; 
— - ethyl, solubility of phenylthiourea in — 
in presence of electrolytes, 250 

Alcohols, influence of water on conduct- 
ance of acids in, 181 

Alloys, compound, conductance of, 396 ; — 
compound, resistance-temperature coeffi- 
cient of, 397 ; — heterogeneous, 393 ; — 
liquid amalgams, conductance of, 397 ; — 
liquid conductance of, 397 ; — liquid, 
conductance of mixtures of sodium and 
potassium, 398 ; — mixed crystals, 393 ; 

— mixed crystals, conductance change 
with composition, 394 ; — mixed crys- 
tals, conductance-temperature coefficient, 
395 ; — properties of, 393 ; — thermal 
conductance of, 403 

Ammonia, conductance of AgCN in, 53 ; — 
conductance of Hg(CN)2 in, 53: — con- 
ductance of higher types of salts in. 
105, 108 ; — conductance of KNO3 in, 
52-; — conductance of solutions in — at 
different temperatures, 145 : — hydrolytic 
equilibria in, 230 ; — molecular weight 
in — solutions, 240 ; — reactions in, see 
Reactions ; — solutions of metallic com- 
pounds in, 215 ; — solutions ot metals 
in, 367 ; — viscosity of, 65 
Ammonium Complex, nature of the, 213 _ 
Anions, complex, 213; — complex, in 
liquid ammonia, 215 ; — complex, nature 

Antimony, complex anion of, 21b 

Bases, organic, free radicals of, 213 ; — or- 
ganic, nature of the positive ions ot, 
213 ; — organic, positive ions 01, /l^ 
Basic 'amides, nature of, 316 
Bromine, conductance of solutions in, 50 

Catalytic action of acids, esteriflcation con- 
stants in methyl alcohol, 289 ; -action 
of alcoholate ion 291 ; — action of elec- 
trolytes Arrhenlus' theory of, 291 , — 
action of hydrogen .ion velocit^constants 
oqn ■ — action of ions. J,»( , — aciiou ul 
ions' as influenced by their thermody- 
namic potential 291 ; -- ^<^^_}^\^l^^°''^i 
Inversion coefficients, 288 — a«^o° ^^ 
iin ionized molecules. 28s , ■ — aciiou, le 
{"a^v^if ions and un-ionized molecules. 
290 



Clausius, ionization according to, 34 
Complexes, formation of — in mixed solvents, 

177 
Compounds, metallic, nature of, 216 
Concentration cells, electromotive force of, 

298 ; — cells, energy effects in, 306 
Conductance, abnormal — of hydrogen and 

hydroxyl ions, 205 ; — dependence of — 

on fluidity at different temperatures, 122 ; 

— equation, constants of, for different 
solvents, 75 ; — equation, constants of, 
tor dilute aqueous solutions, 100 ; — 
equation, constants of, for solvents of low 
dielectric constant, 77 ; — ■ equation, con- 
stants of, in ammonia, 73, 77 ; — equa- 
tion, geometrical interpretation of, 80 ; — 
equivalent, and transference numbers, 32 ; 
— equivalent, defined, 27 ; — equivalent, 
influence of concentration on, 30 ; — 
equivalent, influence of temperature on 
— In sulphur dioxide, 155 ; — equivalent. 
Influence of viscosity on limiting value 
of, 109 ; — equivalent, ionic, 37 ; — equi- 
valent, limiting value of, 30 ; — equi- 
valent, limiting value of, in acetone, 
62 ; — ■ equivalent, limiting value of, in 
alcoholic solutions containing water, 181 ; 

— equivalent, limiting value of. in differ- 
ent solvents, 62 ; — equivalent, limiting 
value of, for organic electrolytes in am- 
monia, 60 ; — equivalent, limiting value 
of, for salts in ammonia, 59 ; — equi- 
valent, of aqueous salt solutions at high 
temperatures, 147 ; — equivalent, of 
higher types of salts at higher tempera- 
tures In water, 148 ; — equivalent, table 
of, 28 ; — function, applicability of — 
to ammonia solutions, 70 ; — function, 
form of, 67 ; — function, form of, in 
dilute aqueous solutions, 98 ; — function, 
graphical treatment of. 69 ; — function, 
Kraus and Bray's, 68 ; — function. 
Storch's, 67 ; — in critical region, 167 ; 
— • in critical region, in methyl alcohol, 
169; — in mixed solvents, 176, 190; — 
in vapors near critical point, 170 ; — 
influence of complex formation on — in 
mixed solvents, 197 ; — Influence of con- 
centration on. 46 ; — influence of density 
of solvent on. 172 ; — influence of tem- 
perature on — at high concentrations, 
166 • — influence of water on — In non- 
aqueous solvents, 178, 179 ; —Influence of 
water on — in solutions of acids In alco- 
hols, 180 ; — ■ ionic, abnormal values of, 
206 ; — ionic, comparison of, in ammonia 
and water. 64 ; — ionic, comparison of, 
in different solvents, 63 ; — ionic, influ- 
ence of temperature on, 123 ; — ionic, 
influence of viscosity on. 111 ; — Ionic, 
table of values of, in ammonia, 64 ; — 
ionic, values of, in formic acid, 207 ; — 
ionic values of, in water, 37 ; — ot fused 
salts, 353; — of glass, 356; — of pure 
substances, 351 ; — of solid electrolytes, 
359 ; — of solutions in non-aqueous sol- 
vents, 46 ; — -temperature coefficient, 
influence of concentration on the, 161 ; — 
-temperature coefficient of solutions in 
halogen acids at high concentrations. 

Conduction process, relation between metal- 
lic and electrolytic, 366 



409 



410 



SUBJECT INDEX 



Conductors, electrolytic, 14 ; — metallic, 

14 384 ; — metallic, anisotropic, 40^ , 

— metallic. Influence of treatment on 
properties of, 402; — metallic, influence 
of pressure on, 402 ; — metallic, photo- 
electric properties of, 402 ; — mixed me- 
tallic and electrolytic, 366; — variable, 
399 

Constant, ionization. Influence of water on 
— of acids in alcohols. 185 . 

Critical point, conductance in neigh Dor- 
hood of, 167 

Density coefllcient of ions, additive nature 
of 286 ; — coeflScient of un-ionized mole- 
cules, 285 ; — of electrolytic solutions, 
283 ; — of electrolytic solutions, as a 
function of ionization, 284 ; —- of elec- 
trolytic solutions, according to Heydweil- 
ler 284 ; — of solutions In acetone, ^sl ; 

— of solutions in ethyl alcohol, 287 ; — 
of solutions in methyl alcohol, 287 , 

Dielectric constant, dependence of ioniza- 
tion on, 89 ; — constant, influence of, on 
conductance, 16 ; — constant, influence 
of, on constants of conductance equation, 
90 • — constant, influence of, on ioniza- 
tion according to Walden, 92 ; — con- 
stant, influence of salts on, 92. 

Diffusion coeflScient of electrolytes, 280 ; —- 
coefllcient of electrolytes, in presence of 
other electrolytes, 282 ; — of electrolytes, 
280 ; — of electrolytes, in presence of 
other electrolytes, 281 

Dilution law, see Conductance function 

Electricity and matter, 17 ; — discrete 

structure of, 20 
Electrolytes, conductance of, in pure state, 

15 ; — ■ diffusion of, 280 ; — equilibria in 
mixtures of, 218 ; — ionization of, 34 ; 
— • molecular weight of, in solution, 37 ; 

— principles applicable to mixtures of, 
220 . 

Electromotive force and conductance meas- 
urements compared, 300 ; — force of 
concentration cells, 297, 298 ; — force 
of concentration cells, numerical values, 
300 ; — force of concentration cells, the- 
ory of, 297 ; — force of concentration 
cells, with mixed electrolytes, 302 

Energy effects in concentration cells with 
mixed electrolytes, 307 

Equilibria, heterogeneous, 232 ; — homo- 
geneous ionic. 218 ; — hydrolytic. 225 ; — ■ 
hydrolytic. equations of, 225 ; — in mix- 
tures with common ion. 219 

Ethyl alcohol, conductance of C0CI2 in— 
at different temperatures, 162 

Ethylamine, conductance of solutions in, 
51 ; — conductance of solutions in, at 
different temperatures, 159 

Faraday's Laws, 19 ; — Laws, applicability 
of, 19 : — Laws, applicability of, to 
metal-ammonia solutions, 20 ; — Laws, 
exceptions to, 20 

Fluidity, see also Viscosity ; — of mixed 
solvents, 187 

Formates, conductance of — compared with 
acetates In water, 102 ; — • solutions of, 
in formic acid, 101 

Freezing point, comparison of — ^tor solu- 
tions of different salts in water, 232 

Fused salts, applicability of Faraday's Law 
to. 353 ; — salts, conductance and fluid- 
ity compared, 354 ; — salts, conductance 
of. 353 ; — salts, conductance of mix- 
tures of, 355 ; — salts. Influence of tem- 
perature on conductance of, 854 



Gases, conduction in, 13 

Glass, conductance of, 356 ; — influence of 
temperature on conductance of, 357 ; — 
Ionization value for, 358 ; — speed of 
ions in, 359 ; — transference in, 357 

Graphite, pure, conductance of, 400 

Hall effect, theory of, 407 

Heat effects in concentration cells, 306 ; 

— of dilution of electrolytes, 305 ; — of 
neutralization of acids and bases, 304 ; — 
of neutralization of acids and bases and 
ionization constant of water, 304 

Hexane, conductance in, 13, 351 
Hittorf's numbers, see Transference 
Hydration, from transference measurements, 
198 : — ■ influence of concentration on, 
201 ; — influence of — on conductance, 
201 ; — influence of temperature on, 125 ; 
— ■ of ions in water, 198, 200 ; — • rela- 
tive — of ions, 201 
Hydrogen bromide, conductance of methyl 
alcohol in, 49 ; — solubility of — in pres- 
ence of electrolytes, 245 
Hydrolysis, see also Equilibria ; — 225 ; — 
at low concentrations in water, 228 ; — ■ 
in phenol, 244 ; — influence of, on con- 
ductance. 228 ; — of salts at high tem- 
peratures, 150 

Insulators, conductance of, 351 

Iodine, conductance of, in sulphur dioxide, 
322 

Ion, chloride, conductance of, in formic 
acid, 207 ; — complex iodide, 214 ; — 
complex sulphide, 214 ; — conductance, 
independence of nature of other ions, 
309 ; — conductance, of chloride ion with 
different cations compared, 309 ; — con- 
ductance, of potassium ion of different 
salts compared, 310 ; — hydrogen, as ox- 
onium complex, 205 ; — hydrogen, con- 
ductance of, in formic acid, 207 ; — hy- 
drogen, in liquid ammonia, 206 ; — 
hydrogen, nature of, 205 ; — hydroxyl, 
2O5 ; — product, constancy of — for 
strong electrolytes, 262 ; — pyridonium, 
conductance of, in pyridine, 208 

Ionic speed, influence of temperature on, 
124 ; — speed. Influence of viscosity on, 
in differerft solvents. 111 

Ionization as a result of compound forma- 
tion, 322 ; — as measured by conduct- 
ance, 34 ; — as related to constitution 
of electrolyte, 320 ; — ■ constant of am- 
monia and acetic acid at elevated tem- 
peratures, 149 ; — constant of water, 
225 ; — constant of water and heat of 
neutralization, 304 ; — constant of water 
at high temperature, 150 ; — dependence 
of, on dielectric constant according to 
Walden, 92 ; — dependence of, on prop- 
erties of solvent, 88 ; — dependence of, 
on solvent, 48 ; — derived from osmotic 
and conductance measurements com- 
pared, 233 ; — factors Influencing, 318 ; 

— influence of temperature on — in water, 
150 ; — of electrolytes, by freezing point 
method, 38 ; — of salts of organic bases, 
321 ; — values, table of. 35 

Ionizing power as depen'Sent on dielectric 
constant. 318 ; — power of solvents in 
critical region, 319 ; — power of solvent 
in relation to constitution, 318 

Ions, catalytic action of, 287 ; — charge on 

— as determined by conditions, 322 ; — 
complex negative, 216 ; — complexity of 
-;-as influenced by temperature, 125 ; — 
dimensions of — as calculated by Born and 
Lorenz, 202 ; — dimensions of — as de- 
rived from conductance. 202 ; — hydra- 
tion of. In water ; see Hydration. 198 ; — 
interaction of, with polar molecules, 198 ; 



SUBJECT INDEX 



411 



— intermediate, 217 ; — iatermediate, 
influence of, on conductance, 104 ; • — in- 
termediate, influence of, on dilution func- 

, Hon, 97 ; — intermediate, influence of, on 
molecular weiglit, 41 ; — nature of — in 
electrolytic solutions, 198 

Isohydric principle, 219 ; — principle, ap- 
plied to solubility data, 262 ; — principle, 
test of, 224 

Law of Kohlrauseh, 33 ; — of mass action, 
applicability of, to ammonia solutions, 5U ; 
-^ of mass action, applicability of, to 
aqueous solutions at higb temperatures, 
158 ; — ■ of mass action, applicability of, 

, , to dilute aqueous solutions, 98 ; — of 
mass action, applicability of, to elec- 
, tjplytes, 41 ; — of mass action, appli- 
cability of, to non-aqueous solutions, 53 ; 

— of mass action, applicability of, to 
solutions in formic acid, 101 ; — of mass 
action, applicability of, to weak elec- 
trolytes, 43 ; — of mass action, devia- 
tions from, in ammonia, 58, 86 ; — ^ of 
mass action, graphical treatment of, 54 ; 

— of mass action, limited applicability 
of, 238 ; — of mass action, theories of 
deriations from, 96 

Lead, complex aition of, 216 

Lithium hydri<^e, conductance of, 364 ; — 

hydride, nature of conduction process in, 

365 

Mass-action constant, dependence of, on di- 

' electric constant, 90 ; — constant, table 

of values of — for different solvents, 62 ; 

— constant, table of values of — for or- 
ganic electrolytes- in ammonia, 60; — 
constant, table of values of — for salts in 
ammonia, 59 ; — constant, table of val- 
ues of — in acetone, 62 ; — function, 
form of, for salts of higher types in am- 
monia, 108 ; — function, in ammonia and 
water compared, 55 ; — function, in am- 
monia solutions, KNOa, 55 ; — function, 
influence of temperature on, 153, 156 ; — 
function, for aqueous KCl solutions, 45 ; 

— function for HCl in water, 45 ; 

— function, variation of, for higher type 
salts in water, 106, 107; — law of, see 
Law . .. . 

Metal-ammonia solutions, ammoniation of 
negative electron in, 374; — solutions, 
atomic conductance of concentrated solu- 
tions, 380 ; — solutions, complexes 
formed in, 367 ; — solutions, conduct- 
ance of sodium in, 376 ; — solutions, equi- 
libria in, 371 ; — solutions, limiting con- 
ductance of negative electron in, 377 ; — 
solutions, method of determining jela- 
■ tlve speed of ions in, 372 ; — solutions, 
molecular weight determinations, 367 , — 
solutions, nature of carriers in, 369; — 
solutions, properties of, 366 ; — solutions, 
relative speed of ions in, numerical val- 
ues, 373; - solutions, specific conduct- 
ance of concentrated solutions in, 37S , 
_ solutions, temperature coefficient of. 
382 ; — solutions, transference effects 

Methyl alcohol, conductance of salts in- 
near critical point, 169 

Methvlamine, conductance of KI in. au , — 
conductance of KI in, at different tem- 
De?atures, 164 ; — conductance of solu- 

B^r^ if-rtfst^n-cfff^f efo 
^flilge of state, 389 ; — change of spe- 



ciflc resistance of — on melting, 388 ; — 
compound, 384 ; — conduction of solu- 
tions of — in ammonia, 20 ; — conduc- 
tion process in, 3*0 ; — ettects in — under 
acceleration, 386 ; — elementary, resist- 
ance-temperature coefficient of, 387, 391 ; 
— _ elementary, resistance-temperature co- 
efficient of, at constant volume, 393 ; — 
elementary, resistance-temperature coeffi- 
cient of, in liquid state, 392 ; — galvano- 
magnetic properties of, 405 ; — Hall er- 
fect in. 406 ; — influence of impurities 
on conductance of, 400 ; — influence of 
temperature on conductance of, 389 ; — 
influence of temperature on conductance 
of, at Igw temperatures, 389 ; — nature 
of, 384 ; — optical properties of, 407 ; — 
properties of, 384 ; — relation between 
thermal and electrical conductance of, 
403 ; — specific resistance of elemeiitar.\ , 
386 ; — state of, 384 ; — supraconducting 
■state of, 390 ; — thermal conductance ot, 
403 ; — ■ thermal conductance of. at low 
temperatures, 403 ; — thermoelectric 
properties in, 404 ; — thermomagnetic 
properties in, 405 ; — transference effects 
in, 385 
Mercury methyl, properties of, 213 
Mixed solvents, conductance in. 120 ; — 

solvents, fluidity of, 187 
Mixtures of electrolytes, equilibria in, 218 ; 

— of electrol.ytes, freezing points of. 234 
Molecular weight, determination of, by 

vapor pressure method, 238 ; — weight, 
from osmotic data. 232 ; — weight in 
non-aqueous solutions, 239 ; — weight 
in sulphur dioxide, 239 ; — weight of 
electrolytes by freezing point method. 38 

— weight of electrolytes in solution, 37 

— weight of electrolytes in water. 232 

— weight of electrolytes, limitation of 
method of determining, by osmotic meth- 
ods, 40 

Optical properties of electrolytes, absorp- 
tion coefficients in water and methyl alco- 
hol. 295 ; — properties of electrolytes, 
absorption curves, 294 ; — properties of 
electrolytes, extinction coefficients of 
acetyloxindon salts in alcohol. 297 ; — 
properties of electrolytes, extinction co- 
efficients of acetyloxindon salts in water, 
296 ; — properties of electrolytes, extinc- 
tion coefficients ot the chromate ion. 293 ; 

— properties of electrolytic solutions, 
292 

Potassium iodide, correction of conduct- 
ance of, for viscosity, 116 

Pressure, influence of, on conductance, 129, 
134 ; — influence of. on conductance, at 
different concentrations, 134 ; — influence 
of, on conductance, due to viscosity 
change in non-aqueous solution. 142 ; — 
influence of. on conductance, in non-aque- 
ous solvents. 139 ; — influence of, on con- 
ductance, of alcohol solutions, 139 ; — 
influence of, on conductance, of different 
electrolytes. 131 ; — influence of. on con- 
ductance of KCl in water. 129 ; — in- 
fluence of. on conductance, of weak elec- 
trolytes, 136 ; — influence ot, on electro- 
lytic conduction, 126ffl — influence of, on 
viscosity of solvent, 126 ; — influence of, 
on viscosity of solutions, 127 

Propyl alcohol. Influence of water on con- 
ductance of solutions In, 178 

Reactions, electrolytic, 16 ; — electroly- 
tic, in ammonia. 314 ; — In ammonia and 
water, compared, 314 ; — in electrolytic 
solutions, 312 ; — in solvents of low di- 
electric constant, 317 



412 



SUBJECT INDEX 



Salts, conductance of higher types of, 104 ; 

— complex metal-ammonia, 209 ; — com- 
plex metal-ammonia, conductance of, 211 ; 

— complex metal-ammonia, ionization of, 
211 ; — complex metal-ammonia, Werner's 
theory of, 210 ; — • fused, see Fused salts ; 

— of higher types, conductance of — at 
higher temperatures in water, 148 ; — 
solid, applicability of Faraday's Law to, 
362 ; — ■ solid, change of conductance at 
transition point, 362 ; — solid, conduct- 
ance of, 359 ; — solid, conductance of, 
at different temperatures, 360 ; — solid, 
conductance of, lithium hydride, see Li- 
thium hydride, 364 ; — solid, conduct- 
ance of mixtures of, 363 ; — ternary, 
conductance of, in ammonia, 105, 108 ; — 
ternary, variation of conductance func- 
tion for — in water, 106 

Sodium acetate, conductance of, in water, 
102 ; — plumbide, electrolysis of, 19 

Solubility experiments, assumptions under- 
lying interpretation of, 264 ; — experi- 
ments, constant concentration of un- 
ionized molecules in, 262 ; — Harklna' 
theory of influence of intermediate ions 
on, 277 ; — Influence of complex ions on, 
267 ; — influence of electrolyte on — in 
ethyl alcohol. 250 ; — of electrolytes in 
presence of common ion, 254 ; — of elec- 
trolytes in presence of other electrolytes, 
254 ; — of electrolytes in salt mixtures, 
BrBnsted's theory of, 337 ; — of gases, 
influence of electrolytes on, 239 ; — of 
higher types of salts, theory of, 275 ; — 
of lithium carbonate in presence of non- 
electrolytes, 252 ; — of non-electrolytes 
in presence of electrolytes, 245 ; — of 
non-electrolytes, influence of electrolytes 
on, 249 ; — of non-electrolytes, influence 
of organic salts on, 250; — of salts in 
presence of non-electrolytes, 251, 253 ; — 
of salts in presence of other salts, lan- 
thanum iodate, 274; — of salts in pres- 
ence of other salts, lead iodate, 270 ; — 
of salts in presence of other salts, silver 
sulphate, 268 ; — ■ of salts in presence 
of other salts, strontium chloride, 271 ; 

— of salts in salt mixtures, ther- 
modynamic treatment, 335 ; — of salts 
of high type in presence of other salts, 
268 ; — of strong electrolytes in pres- 
ence of other electrolytes without com- 
mon ion, 268 ; — of strong electrolytes 
in presence of other strong electrolytes, 
261 ; — of TlCl in presence of other elec- 
trolytes, 261 ; ■ — of weak acids in pres- 
ence of other acids, 256 

Solutions, aqueous, molecular weight in, 
232 ; — electrolytic, 15 ; — electrolytic, 
conductance of, 26 ; — electrolytic, den- 
sity of, 283 ; — electrolytic, equilibria in, 
16 ; — electrolytic, non-aqueous, 46 ; — 
electrolytic, optical properties of, 292 ; — 
electrolytic, reactions in, 16, 312 ; — 
electrolytic, thermal properties of. 303 ; 
— electrolytic, various properties of, 280 ; 

— non-aqueous, molecular weight in, 239 
Solvents, mixed, conductance in, 176 ; — 

mixed, ionization in, 177 ; — pure, con- 
duction process in, 352 
Sulphur dioxide, conductance of KI in, 47 ; 

— dioxide, conductance of solutions in — 
at different temperatures, 155 ; — dioxide, 
molecular weight of solutions In, 239 

Tellurium, complex anion of, 215 
Temperature, conductance of aqueous solu- 
tions at elevated, 146 : — Influence of, 
on conductance, 122, 144 ; — influence 
of. on conductance of ammonia solutions, 
145 ; — influence of. on conductance of 
methylamine solutions, 146 ; — influence 



of, on conductance of non-aqueous solu- 
tions, 154 ; — influence of, on conduct- 
ance of solutions, 51 ; — Influence of, on 
conductance of solutions in 'amines, 159 ; 

— influence of, on constants of con- 
ductance equation, 156 ; — influence of, 
on ionization constants, 149 ; — influence 
of, on ionization of salts, 150 

Theories of electrolytic solutions, miscel- 
laneous, 347 ; — relating to electrolytic 
solutions, 323 

Theory, ionic, 17 ; — ionic, origin of, 21 ; — 
of Berzelius, 20 ; — of electrolytic solu- 
tions, from thermodynamic standpoint, 
324 ; — of electrolytic solutions, Ghosh's, 
340 ; — of electrolytic solutions, Ghosh's, 
compared with experiments, 341 ; — 
of electrolytic solutions. Hertz's, 345 ; 

— of electrolytic solutions. Inconsisten- 
cies in, 328 ; — of electrolytic solutions, 
Jahn's, 326 ; — of electrolytic solutions, 
limitations of — for strong electrolytes, 
323 ; — of electrolytic solutions, Malm- 
strfim's and KJellin's, 339 ; — of elec- 
trolytic solutions, Milner's, 343 ; — of 
electrolytic solutions, present state of, 
summarized, 349 ; — - of Grottbuss, 206 ; 

— of Werner, 210 

Thermal properties of electrolytic solutions, 
303 

Thermodynamic potential of lelectrolytes 
and electromotive force, 298 ; — proper- 
ties of electrolytic solutions, 328 ; — 
properties of electrolytic solutions, nu- 
merical values, 333 

Transference effects accompanying the cur- 
rent, 21 ; — numbers, by moving bound- 
ary method, 23 ; — numbers, change of, 
at low concentrations, 307 ; — numbers, 
change of, for strong acids, 307 ; ■ — ■ num- 
bers, definition of, 21 ; — numbers, in 
ammonia, 64 ; — ■ numbers, influence of 
complex ions on, 24 ; — numbers, influ- 
ence of concentration on, 24 ; — numbers, 
influence of hydration on, 22, 198 ; — 
numbers, influence of temperature on, 26 ; 

— numbers, methods of determining. 22 ; 

— numbers, table of, 25 ; — numbers, 
true. 200 ; — numbers, true, relation of 
— to ordinary, 199 

Van't Hoflt's factor, 38 ; — factor, limiting 
value of, 41 

Variable conductors, change of conductance 
at transition points, 401 ; — conductors, 
specific conductance of, 400; — conduc- 
tors, thermal conductance of, 403 

Velocity of reactions as influenced by Ions, 
287 

Viscosity change due to salts In different 
solvents, 112 ; — change, influence of — 
due to non-electrolytes, on conductance, 
119, 121 : - — dependence of — on dielec- 
tric constant, 112 ; — effect, correction 
of conductance for, 114 ; — effect, nega- 
tive, 113 ; — influence of concentration 
on. 112 ; • — influence of on conductance, 
111 : — influence of, on conductance in 
mixed solvents, 176 ; — influence of on 
conductance in non-aqueous solutions, 
118 ; - — influence of, on conductance of 
concentrated solutions. 118 ; — influence 
of on conductance of different Ions, 114 ; 
— infiuence of, on ionic speeds in different 
solvents. Ill ; — influence of, on Ao 
values, 109 ; — influence of pressure on 
— in different solvents. 143 ; — influence 
of temperature on. 113 ; — of ammonia 
at boiling point. 65 ; — of fused salts, 
354 ; — of mixed solvents, 177 

Water, influence of — on conductance of 
acids in alcohols. 180, 186 ; — Ioniza- 
tion constant of, 225 



NAME INDEX 



Acree, 291 ; — see Loomls ; — see Eobert- 

Bon 
Adams, 233, 234, 343 ; — and Lanman, see 

Lewis 
AkerlOf 292 

AUmand and Polack, 300, 334 
Amagat, 130 
Andrews, see Kendall 
Archibald, 49, 165, 205 ; — and Mcintosh, 

see Steele 
Argo, see Gibson 
Arrhenlus, 17, 18, 21, 34, 37, 38, 42, 54, 219, 

221. 225, 267, 280, 281, 287, 291 
Avogadro, 341 

Baedeker, 385 

Baldwin, see Cady 

Bancroft, 68 

Bates, 69 ; — and Vlnal, 19 

Beattie, see Maclnnes 

Bedford, 233 

Bekier, see Bruner 

Benedicks, 388 

Benrath and Walnoft, 364 

Berzelius, 20, 21 

Blitz, 249, 367 

Bingham and McMaster, see Jones 

Bishop, see Kraus 

Bisson, see Randall 

BJerrum, 331, 337 

Blanchard, 119 

Born, 202, 203, 204 

BBttger, 228 

Bousfleld and Lowry, 114 

Brann, 249 

Braune, 185 , „ ^ 

Bray, 68, 266 ; — see Kraus ; — and Hunt, 

222, 267 ; — and MacKay, 214 ; — and 

Wlnnlnghoff, 261, 262, 265 
Brldeman, 390 , , 

Brighton and Sebastian, see Lewis 
Brensted, 331. 333, 337. 338, 339 
Bruner and Bekier, 322; — and Galecki, 

322 
Bruyn, Lobry de, 198 
Buchbock, 198 
Bunting, see Schlesinger 

Cady, 367. 373; — »ee Franklin — and 
Baldwin, 317 ; — and Llchtenwalter, 317 
Caldwell, see Hantzsch 
Callis, 321, 353 ; — and Greer, 318 
Calvert, see Schlesinger 
Carlisle, see Nicholson 
Cavanagh, 343 
Centnerszwer. see Walden 
Chapman and George, 340 
Chin. 215 
Chow. 303 
Clark. 121 
Claiislus. 34 
Clay, 389. 400. 406 

cSaHe^M?-'- - «'^''--- 
Crommelin. 389 
Cushman, see Randall 

Dalton. 326 

Kt?bT'49f7l. 357 358 
pavis and Jones. 113 



Davy, Sir Humphrey. 19 
Dawson and Fowls. 290 
de Bruyn, Lobry, 198 
Dennison and Steele, 310, 311 
de Szyszkowskl, 69 
Dewar and Fleming, 400 
Drude, 407 ; — and Nernst, 284 
Dummer, 204 

Dutolt and Eappeport. 47 ; — and Levrler, 
47 

Eastman, see Noyes 

Bggert, see Tubandt 

Einstein. 202, 204 

Ellis. 300. 306. 307 ; — see Noyes 

Essex and Rfeaeham, see Loomis 

Euler, 248. 249 

Eversheim, 319 

Falk, see Noyes 

Fanjung, 136 

Faraday, 14. 17, 19. 20. 21, 33. 206, 353, 
357, 362, 363 

Fenninger, 397 

Ferguson, see Tolman 

Fitzgerald. 50. 51, 109. 112, 119. 158, 163 

Fleming, see Dewar 

Foote and Martin. 353 

Forbes. 268 

Franklin, 47, 52, 69. 108. 155. 161, 206. 207, 
230. 315. 316, 373 ; — and Cady. 64 ; — 
and Kraus, 52. 53. 55. 105. 145. 206, 
240. 316 ; — and Stafford, 206, 316 

Franz, see Wiedemann 

Frazer and Sease. see Lovelace 

Galeckl. see Bruner 

Gates, 317. 318 

Geffcken. 245 

George, see Chapman 

Georglevics. 324. 348 

Ghosh, 324. 340. 341. 342, 343 

Gibba. 325. 326 

Gibson and Argo. 367 

Goldschmidt. 180, 182. 183; — and Thue- 

sen. 181, 183, 184. 289 
Goodwin nnd Mailey, 353. 355 
Gordon, 249 
Graetz, 407 
Green, 121 
Greer, see Callis 
Gross, see Kendall 
Grotthuss. 206 
Guertler. 393 

Hall. 386. 406. 407 ; — and Harkins. 233. 

234. 235 
Hantzsch. 293. 295, 296; — and Caldwell, 

206. 208 _ „ „ 

Harkins. 41. 269. 275. 277; — see Hall: 

— and Pearce. 273 „_ _„^ 

Harned. 291. 292, 300. 303. 306, 307, 331, 

335 
Hartung, 242 
Heberlein. see Kiister 
Helmholtz. 17. 20 
Herty. see Werner 
Hertz. 345. 346. 347 
Heuse. 239 „ „„, „„„ 

Heydweiller. 283. 284. 285. 286: — see 

Kohlrausch ; — and Kopfermann. 358 



413 



414 



NAME INDEX 



Hine, 397 

Hlttorf, 21, 22, 23, 24, 34, 206, 345, 348 

Hof, see Onnes 

Holborn, see Kohlrausch 

Hoist, see Onnes 

Hugot, 215 

Hunt, see Bray 

Jaeger and Kapma, 355 

Jaffg, 351 

Jahn, 326, 327, 328 

Johnston, 110, 114, 122 

Jones, see Davis ; — and Veazey, 187, 190 ; 

— Bingham and McMaster, 187, 190, 191, 

192, 194 

Eailan, 183 

Kahlenberg, 317 

Kanolt, 225; — see Morgan 

Kate, see Noyes 

Kendall, 43, 256, 263, 267 ; — and Andrews, 
260 ; — and Gross, 321 

Kerschbaum, see LeBlanc 

Keyes and WinninghofE, 74 

Kjellin, 339 

Koenigsberger, 385, 397, 398, 402, 404, 408 

Kohlrausch, 33, 34, 110, 224 ; — and Hevd- 
weiller, 225, 352 ; — and Holborn, 27 

Kohnstamm, see Van der Waals 

Kopfermann, see Heydweiller 

KBrber, 129. 131, 134 

Kraus, 20, 44, 68, 84, 98, 100, 111, 116, 
123, 146, 168, 172, 213. 216. 322, 340, 
343, 367, 376, 381, 382, 384, 393 ; — and 
Bishop, 178 ; — and Bray. 52. 56. 58, 60, 
61, 64, 68, 70. 72, 74, 77, 82. 98, 109, 
208 ; — and Lucasse, 378, 381 ; — see 
Franklin 

Kurtz, 74, 243 

Kiister, 214 ; — and Heberlein, 214 

Lanman and Adams, see Lewis 

Lattey, 92 

LeBlanc and Kerschbaum, 357 

Levrler, see Dutoit 

Lewis, 23, 308, 331 ; — Adams and Lan- 
man, 385 ; — Brighton and Sebastian, 
300; — and Randall, 330, 332, 333, 335, 
337, 345 

Lichtenwalter, see Cady 

Linhart, 300 

Lodge, 23 

Loomls and Acree, 300 ; — Essex and 
Meacham, 300 

Lorenz, 202, 203, 204, 347, 356, 403 ; — see 
Tubandt 

Lovelace, Frazer and Sease, 238 

Lowenherz, 225 

Lownds, 402 

Lowry, see Bousfield 

Lucasse, 206, 380, 383 ; — see Kraus 

McBain and Coleman, 242 

McCoy and Moore, 213, 384 ; — and West, 

398 
MacDougair, 68 
MacKay, see Brav 
Maclnnes, 308, 309 ; — see Washburn ; — 

and Seattle, 300 ; — and Parker, 301 
Mcintosh and Archibald, see Steele 
McLauchlan, 249 

McMaster and Bingham, see Jones 
Magle, 283 
Mailev. see Goodwin 
Malmstrfim, 339 

^Martin, see Foote ; — see Schlesinger 
Mpflcham and Essex, see Loomis 
^felcher, see Noyes 
^riI]ard, 307 ; — see Washburn 
I\rilner, 337, 343, 344, 347 
Mners. 364 
Moissan, 319 
Mogre, see McCoy 



Morgan and Kanolt, 198 
Mullinix, see Schlesinger 

Nernst, 89, 225, 238, 245, 280, 299, 302, 
326, 328; 339, 401 ; — see Drude 

Nicholson and Carlisle, 19 

Noyes, 146, 148, 149, 150, 152, 267, 304, 
308, 340 ; — and Eastman, 41, 148 ; — 
and Ellis, 300 ; — and Falk, 24, 26, 30, 
35, 37, 38, 114, 232, 309, 310, 337 ; — and 
Kato, 308 ; — and Melcher, 228 ; and 
Sammet, 308 

Ohm, 22, 352 
Oholm, 121, 204, 280 

Onnes, Kammerlingh, 389, 406 ; — and 

Hof, 400 ; — and Hoist, 403 
Ostwald, 287, 288, 348 

Ottiker, 208 

Palmaer, 213, 384 

Parker, see Maclnnes 

Partington, 340 

Patroni, see Poma 

Pearce, see Harkins 

Peck, 19, 216 

Peltier, 404 

Planck, 136, 137, 141, 326 

Plotnikow and Rokotjan, 79 

Polack, see AUmand 

Poma, 302 ; — and Patroni, 302 

Poole, 352 

Powis, see Dawson 

Ramstedt, 290 

Randall, see Lewis ; — and Bisson, 305 ; — 

and Cushman, 300 
Raoult, 38 
Rappeport, see Dutoit 
Reed, see Schlesinger 
Reychler, 348 
Richards and StuU, 19 
Richarz, 388 
Riesenfeld, 242 

Rimbach and Weitzel. 162, 163 
Robertson and Acree. 207 
Roemer, see Thiel 
Rohrs. 287 

Rokotjan, see Plotnikow 
Rontgen, 127 
Rothmund. 245, 249, 252 
Rupert, 353 
Ruthenberg. 287 
Ryerson, 121 

Sachs, see Warburg 

Sack. 145 

Sammet, see Noyes 

Sammis, 317 

Schlesinger. 101. 102, 103. 230; — and 
Calvert, 101, 208 ; — and Bunting. 101, 
207 ; — and Coleman. 101 : — and Mar- 
tin. 101, 207 ; — and Mullinix, 101 ; — 
and Reed, 101 

Schmidt, 139, 141, 142 

Sease and Frazer. see Lovelace 

Sebastian and Brighton, see Lewis 

Serkov, 242 

Setschenow, 249 

Smith, see Stearn ; — Steam and Schnei- 
der, 305 

Smyth, 19, 216, 322 

Snethlage. 324 

Somerville, 393, 396 

Sprung. 112 

Stafford, see Franklin 

Steele, see Dennlson ; — Mcintosh and 
Archibald, 206, 347 

Steam and Schneider, see Smith ; — and 
Smith, 305 

Stelner, 249 

Stewart, see Tolman 

Stieglitz, 864, 26T 



NAME INDEX 



415 



Stokea, 202, 204 
Storch, 07, 68, 69, 98, 348 
Stull, see Richaras 
SzyszkowsUi, de, 69 

Tammann, 129, 131, 130, 137, 138 

Taylor, 290 

Tegetmeier, see Warburg 

Thiol and Eoemer, 230 

Thomson, J. J., 390, 406, 407 

Thomson, Sir William, 89, 339, 404 

Thorin, 250 

Thuesen, see Goldschmidt 

Tibbals, 214 

Tolman, 297 ; — and Ferguson, 300 ; — and 

Stewart, 386 
Tubandt, 363 ; — ■ and Eggert, 363 ; — and 

Lorenz, 19, 355, 356, 360, 362, 364 

Van der Waals, 42, 325, 326 

van Everdingen. 402 

van't Hoffi, 38, 239, 337, 343 



Veazey, see Jones 
Vinal, see Bates 

Wainoff, see Benrath 

Walden, 92, 93, 95, 110, 241, 320, 322 ; — 

and Centnerszwer, 146, 239 
Warburg and Sachs, 127 ; — • and Teget- 

meier, 359 
Washburn, 26, 43, 99, 100, 114, 121, 198, 

199, 228, 239 ; — and Maclnnes, 232 ; — 

and Millard, 198 ; — and Weiland, 98 
Weiland, 44 ; — see Washburn 
Weitzel, see Rimbach 
Werner, 210, 211, 217, 312; — and Herty, 

211 
West, see McCoy 
Wiedemann and Franz, 403 
Wljs, 225 

Wlnkelmann, 385, 407 
Winninghoff, see Bray ; — see Keyes 
WOrmann, 304 

Zeittuchs, 215